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Clemson UniversityTigerPrints
All Dissertations Dissertations
12-2016
Interface Shear Transfer in Reinforced ConcreteMembers: Code Evaluation, Modeling, and TestingMahmoodreza SoltaniClemson University, msoltan@g.clemson.edu
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Recommended CitationSoltani, Mahmoodreza, "Interface Shear Transfer in Reinforced Concrete Members: Code Evaluation, Modeling, and Testing" (2016).All Dissertations. 1819.https://tigerprints.clemson.edu/all_dissertations/1819
INTERFACE SHEAR TRANSFER IN REINFORCED CONCRETE MEMBERS:
CODE EVALUATION, MODELING, AND TESTING
A Dissertation
Presented to
the Graduate School of
Clemson University
In Partial Fulfillment
of the Requirements for the Degree
Doctor of Philosophy
Civil Engineering
by
Mahmoodreza Soltani
December 2016
Accepted by:
Dr. Brandon E. Ross, Committee Chair
Dr. Thomas E. Cousins, Committee Co-Chair
Dr. Weichiang Pang
Dr. Amin Khademi
ii
ABSTRACT
Transfer of shear forces across concrete-to-concrete interfaces is critical to the
strength of many reinforced concrete structures. One common example is the horizontal
interface between precast concrete girders and cast-in-place concrete bridge decks.
Composite action between the girder and deck, and thus bridge stiffness and strength,
relies on the capacity of the interface to transfer shear forces. This concept is explained
through Interface Shear Transfer (IST) theory. In this dissertation, trinary objectives are
presented to describe and scrutinize this theory. These objectives include evaluating the
current code-based IST models, creating a new IST model, and demonstrating a new
method for experimentally testing IST.
Firstly, a database of IST experiments on uncracked reinforced concrete
specimens was created from published test results. A total of 774 tests were reviewed,
with data coming from tests conducted between 1969 and 2014. Once compiled, the
database was used to evaluate the accuracy of the interface shear transfer provisions from
the AASHTO LRFD Bridge Design Specifications, Eurocode 2, and CSA A23.3.
Through this evaluation it was determined that experimental capacities were an average
of 1.49, 1.93, and 2.83 times greater than the code-calculated nominal capacities for the
LRFD, Eurocode, and CSA codes, respectively. While each of the codes was
conservative on average, the degree of conservatism was found to be dependent on design
variables such as concrete compressive strength, amount of interface reinforcement, and
member size.
iii
In the first phase of the dissertation, it was shown that current code-based IST
models produce inconsistent levels of accuracy for different values of design variables. In
the second phase, sensitivity analyses were performed to identify the variables having the
greatest impact on the IST capacity, and to create a design model that produces consistent
levels of accuracy. Using a database of experimental results, an Artificial Neural Network
(ANN) model was created to estimate IST strength and to perform a sensitivity analysis
of the design variables. The sensitivity analysis demonstrated that compressive strength
was the most significant variable affecting IST capacity. A multiple linear-regression
analysis was also performed to aide in development of a new design model. Based on the
results of the sensitively analysis, the new model directly accounted for compressive
strength of concrete as one of the model variables. The model was strongly correlated
with the experimental data and produced consistent levels of accuracy for a range of
design variables.
Finally, IST test methods were scrutinized and a new IST test method was
proposed. Traditionally, IST capacity has been tested using a push-off test method, in
which direct shear is induced through compression loads placed at the ends of notched
test specimens. In this research, the 4-point bending test method, as proposed by
Iosipescu in 1967, was investigated to study IST. The 4-point bending test created direct
shear by strategically placing the supports and loads on a beam. It had the advantages of
using test specimens that were easier to assemble. Additionally, it produced a more
uniform stress state at the interface compared to the interface stress distribution of the
push-off test, making the 4-point bending test a better representation of the stress state at
iv
cast-in-place deck and bridge girder connections. In this study, these two test methods
were compared and contrasted through an experimental program along with analytical
modeling. The conditions in which the proposed test method was an acceptable
alternative for the push-off method were identified.
v
DEDICATION
This dissertation is dedicated to my kind mother, Fatemeh Pahlavani, and my
supportive father, Nosratollah Soltani, for their unreserved dedication to my success.
Without their loving support, I could not have made it this far or written this dissertation.
vi
ACKNOWLEDGMENTS
First, I would like to wholehearted thank my advisors, Dr. Brandon E. Ross and
Dr. Thomas E. Cousins, for their continuous and patient support of my PhD study. Their
guidance greatly improved the quality of my research and led to the writing of this
dissertation. In addition to my advisors, I also would like to thank the rest of my PhD
committee, Dr. Weichiang Pang and Dr. Amin Khademi, for their helpful comments and
guidance.
Glenn Department of Civil Engineering lab supervisor Daniel Metz, his crew, and
also Clemson University graduate students Luay Abo-Alarab, Indika Mapa, Sachin
Sreedhara, Shreyas Indurkar, and Mikayla Bladow are gratefully acknowledged for their
assistance during experimental phase of this dissertation.
Last, but not least, I would like to thank my parents for helping me realize my
potential by emotionally supporting me in the writing of this dissertation and in my life in
general.
vii
TABLE OF CONTENTS
Page
TITLE PAGE .................................................................................................................... i
ABSTRACT ..................................................................................................................... ii
DEDICATION ................................................................................................................. v
ACKNOWLEDGMENTS .............................................................................................. vi
LIST OF TABLES .......................................................................................................... ix
LIST OF FIGURES ......................................................................................................... x
CHAPTER
I. INTRODUCTION ......................................................................................... 1
Interface Shear Transfer ........................................................................... 1
Research Objective and Scope ................................................................. 3
Dissertation Organization ........................................................................ 4
References ................................................................................................ 5
II. DATABASE EVALUATION OF INTERFACE SHEAR TRANSFER IN
REINFORCED CONCRETE MEMBERS .............................................. 6
Introduction .............................................................................................. 6
Research Significance .............................................................................. 7
Background .............................................................................................. 8
Code Provisions for Interface Shear Transfer ........................................ 11
Interface Shear Transfer Database ......................................................... 17
Filtering Processes ................................................................................. 17
Code-Specific Database Characteristics ................................................ 20
Evaluation of Codes ............................................................................... 21
Overall Evaluation ................................................................................. 22
Detailed Evaluation ................................................................................ 25
Summary and Conclusions .................................................................... 31
Notation.................................................................................................. 34
References .............................................................................................. 35
viii
Table of Contents (Continued)
Page
III. A STATISTICAL APPROACH TO REFINE DESIGN CODES FOR
INTERFACE SHEAR TRANSFER IN REINFORCED CONCRETE
STRUCTURES ...................................................................................... 42
Introduction ............................................................................................ 42
Background ............................................................................................ 44
Interface Shear Transfer Database ......................................................... 48
Evaluation Using Artificial Neural Network ......................................... 49
Proposed Interface Shear Transfer Model ............................................. 53
Summary and Conclusions .................................................................... 62
Notation.................................................................................................. 64
References .............................................................................................. 65
IV. EVALUATION OF A 4-POINT BENDING TEST METHOD FOR
INTERFACE SHEAR TRANSFER IN CONCRETE MEMBERS ...... 69
Introduction ............................................................................................ 69
Background ............................................................................................ 71
Analytical Program ................................................................................ 75
Experimental Program ........................................................................... 79
Summary and Conclusions .................................................................... 88
References .............................................................................................. 89
V. SUMMARY AND CONTRIBUTIONS ...................................................... 92
APPENDICES ............................................................................................................... 96
APPENDIX A: List OF REFERENCES FOR THE ACI DATABASE PAPER AND
DATABASE EVALUATION ....................................................................................... 97
ix
LIST OF TABLES
Table Page
Chapter 2
Table 1- Factors for LRFD ............................................................................................ 13
Table 2- Factors for Eurocode ...................................................................................... 15
Table 3- Factors for CSA ............................................................................................... 16
Table 4- Distributions of experimental variables in code-specific databases ............... 21
Table 5-Summary of code comparisons ......................................................................... 24
Table 6- Bin evaluation of experimental variables ........................................................ 28
Chapter 3
Table 1- The range of input parameters ........................................................................ 50
Table 2- Coefficients of the proposed model ................................................................. 55
Table 3- Statistical parameters of the regression analysis ............................................ 56
Table 4- Results of the t-test for with and without reinforcement populations .............. 57
Table 5- Comparison of the proposed model with the design codes ............................. 59
Chapter 4
Table 1- Test matrix of experimental program .............................................................. 79
Table 2-Material properties ........................................................................................... 81
Chapter 5
Table 1- Key findings and significance of different phases in this study ....................... 93
x
LIST OF FIGURES
Figure Page
Chapter 1
Fig. 1- Interface shear transfer between precast girder and cast-in-place ..................... 1
Fig. 2- Interface Shear Transfer, saw-tooth model (after Santos and Júlio 2012 [1]).... 2
Fig. 3- Iosipescu V-Notched 4-point bending test method ............................................... 4
Fig. 4- Conventional IST test method, Push-Off .............................................................. 4
Chapter 2
Fig. 1- Interface shear transfer between precast girder and cast-in-place deck ............. 7
Fig. 2- Interface Shear Transfer (after Santos and Julio [35]) ....................................... 9
Fig. 3- Filtering process of the database ....................................................................... 18
Fig. 4- Test methods ....................................................................................................... 19
Fig. 5- Distributions of interface shear transfer strength ratio ..................................... 23
Fig. 6- Interface shear transfer strength ratios compared to experimental variables .. 27
Fig. 7- Interface shear transfer strength ratios compared to concrete unit weight and
surface roughness. Boxes indicate the upper and lower quartile of scatter, whiskers
indicate the range. ......................................................................................................... 30
Chapter 3
Fig. 1- Interface shear transfer between precast girder and cast-in-place deck ........... 42
Fig. 2- Interface Shear Transfer, saw-tooth model (after Santos and Júlio 20125) ...... 45
Fig. 3- Schematic of ANN model.................................................................................... 51
Fig. 4- ANN performance for the entire database (1 kip= 4.448 kN) ........................... 51
Fig. 5- IST sensitivity analysis using ANN model .......................................................... 52
xi
List of Figures (Continued)
Figure Page
Fig. 6- Multiple linear-regression performance of the proposed (1 kip= 4.448 kN) .... 56
Fig. 7- IST strength ratios compared to experimental variables. .................................. 58
Fig. 8- Comparison of the performance of the proposed model (PM) and LRFD, EC,
and CSA through moving average of datasets ............................................................... 60
Fig. 9- Percentage of unconservative results for different SAF. ................................... 62
Chapter 4
Fig. 1-Interface shear transfer between precast girder and cast-in-place deck ............ 70
Fig. 2- Conventional IST test method, push-off ............................................................. 70
Fig. 3- V-Notched Iosipescu 4-point bending test method ............................................. 71
Fig. 4-Saw-tooth model (after Santos and Julio [4]) ..................................................... 72
Fig. 5- Interface shear transfer test methods ................................................................. 74
Fig. 6- Horizontal set-up of the Push-Off test................................................................ 74
Fig. 7- Meshing, boundary condition, and loading configuration of analytical program,
VN model (left) and PO model (right) ........................................................................... 76
Fig. 8- Shear stress (left) and normal stress (right) for PO vs. VN ............................... 77
Fig. 9- Mesh convergence study of Shear stress (left) and normal stress (right) for PO vs.
VN (the squares show the point used to conduct the convergence study) ..................... 78
Fig. 10- Nomenclature of test specimens ....................................................................... 80
Fig. 11- Loading configuration of experimental program, VN test (left) and PO test
(right)………… ............................................................................................................. 81
Fig. 12- Installment configuration of string pods, VN test (left) and PO test (right) .... 82
Fig. 13- Reinforcement plan of experimental program, VN (left) and PO (right)......... 83
xii
List of Figures (Continued)
Figure Page
Fig. 14- Stiffeners attached to the PO specimens .......................................................... 84
Fig. 15- Results of the experimental program ............................................................... 85
Fig. 16- Interface shear versus interface horizontal slip graphs ................................... 86
Fig. 17- Binding in the smooth interface of VN tests and application of normal force . 87
1
CHAPTER ONE
INTRODUCTION
Interface Shear Transfer
Transfer of shear forces across concrete-to-concrete interfaces is critical to the
strength of many Reinforced Concrete (hereafter referred to as “RC”) structures. The
horizontal interface between precast concrete girders and cast-in-place concrete bridge
decks is an example of a situation where this concept must be considered (Fig. 1). A
bridge’s superstructure is usually built in two phases. Firstly, the girders are placed, and
the bridge deck is constructed over them. Transfer of the shear force from the deck to the
girders plays an important role for load-carrying capacity of the structure. Composite
action between the girder and deck, and thus bridge stiffness and strength, relies on the
capacity of the interface to transfer shear forces. The Interface Shear Transfer (Hereafter
referred to as “IST”) theory explains the concept.
Fig. 1- Interface shear transfer between precast girder and cast-in-place deck
2
Shear forces are carried across concrete-to-concrete interfaces through three
mechanisms including: 1) shear-friction, 2) cohesion between concrete surfaces, and 3)
dowel action of reinforcement [1],[2]. The shear-friction concept was initially proposed
by Mast (1968)[3] and Birkeland and Birkeland (1966)[4] to explain shear force transfer
across cracks in RC members. Shear-friction can be explained using a saw-tooth model
[1], as illustrated in Fig. 2. Shear force causes horizontal displacement, h, between two
concrete surfaces. The horizontal displacement is accompanied by vertical displacement,
v, due to concrete interlock. Vertical displacement causes tension in steel reinforcement
crossing the interface; this tension results in a clamping force and friction along the
interface. Cohesion is the bond between concrete interface surfaces. Dowel action is due
to the direct shear resistance of the reinforcement crossing the interface. When load is
small shear force is resisted almost exclusively through cohesion. However, at higher
loads cracks form as cohesion is broken, and forces are carried through a combination of
shear-friction and dowel action [1].
Fig. 2- Interface Shear Transfer, saw-tooth model (after Santos and Júlio 2012 [1])
Concrete
Layer 2
Concrete
Layer 1
Interface
Reinforcement
3
Research Objective and Scope
This research is conducted in three phases. First, among all the research on the
IST, there has been no comprehensive database that can be used to compare and validate
design models. Such a database is created in the current research and is used to evaluate
the IST provision of design codes including AASHTO LRFD 2014 [5], Eurocode 2 2004
[6], CSA A23 2014 [7]. The accuracy, coefficient of variation, consistency level of
accuracy of each code are scrutinized across the range of design variables including the
compressive strength of concrete, reinforcement index, and interface cross-section area.
Potential issues and limitations of the current codes are identified and discussed.
In the second phase, a sensitivity analysis using Artificial Neural Networks
(Hereafter referred to as “ANNs”) is conducted to elucidate the relation of variables to
IST capacity. The analysis is also used to determine the most influential variables
affecting IST capacity. Subsequent to the sensitivity analysis, multiple-linear regression
analysis is used to create a new IST design model. The proposed model is more accurate
and consistent in comparison with the aforementioned design codes.
In the third phase, this research evaluated the Iosipescu V-Notched 4-point
bending test (Fig. 3) [8] for testing IST. This test is compared and contrasted with the
more conventional push-off method (Fig. 4). Experimental and numerical analyses are
used to compare and contrast these two test methods. The experimentation pros and cons
in addition to the observed specimen behavior of these two test methods are presented.
4
Fig. 3- Iosipescu V-Notched 4-point bending test method
Fig. 4- Conventional IST test method, Push-Off
Dissertation Organization
In this dissertation, Chapters 2, 3, and 4 are written as stand-alone technical
papers. Chapter 2 corresponds to the first phase of the research. In this chapter the results
of experimental studies on interface shear transfer available in literature are reviewed and
are compiled into a database. Evaluations of AASHTO LRFD 2014, Eurocode 2 2004,
5
and CSA A23 2014 specifications for IST are also presented. Chapter 3 corresponds to
the second phase of the research, and presents a sensitivity analysis and also proposes a
new IST model. Chapter 4 describes the third phase of research. Comparison results of
two IST test methods are presented in Chapter 4. Chapter 5 contains conclusions and
recommendations of the study.
References
[1] P. M. Santos and E. N. Júlio, “A state-of-the-art review on shear-friction,”
Engineering Structures, vol. 45, pp. 435–448, 2012.
[2] R. Jimenez-Perez, P. Gergely, and R. N. White, “Shear transfer across cracks in
reinforced concrete,” Cornell Univ., Ithaca, NY (USA), 1978.
[3] R. F. Mast, “Auxiliary reinforcement in concrete connections,” Journal of the
Structural Division, 1968.
[4] P. W. Birkeland and H. W. Birkeland, “Connections in precast concrete
construction,” in ACI journal, Proceedings, 1966, vol. 63, pp. 345–367.
[5] AASHTO, “AASHTO LRFD Bridge Design Specifications,” 7th ed., AASHTO,
2014.
[6] British Standards Institution, “Eurocode 2: Design of Concrete Structures,” in
Eurocode 2: Design of Concrete Structures, 2004.
[7] Canadian Standard Association, “CSA Standard A23.3-14,” Canadian Standard
Association, 2014.
[8] N. Iosipescu, “New accurate procedure for single shear testing of metals,” J MATER,
vol. 2, no. 3, pp. 537–566, 1967.
6
CHAPTER TWO
DATABASE EVALUATION OF INTERFACE SHEAR TRANSFER IN
REINFORCED CONCRETE MEMBERSi
INTRODUCTION
Transfer of shear forces across concrete-to-concrete interfaces is critical to the
strength of many reinforced concrete structures. One common example is the horizontal
interface between precast concrete girders and cast-in-place concrete bridge decks (Fig.
1). Composite action between the girder and deck, and thus bridge stiffness and strength,
relies on the capacity of the interface to transfer shear forces.
The objective of this paper is to evaluate code-based interface shear transfer
design procedures through comparison with a database of experimental tests. The
database was created from test results published in North America and Europe. Three
codes were evaluated: AASHTO LRFD Bridge Design Specifications (hereafter
"LRFD")1, Eurocode 2: Design of Concrete Structures (hereafter "EC")2, and CSA
A23.3: Design of Concrete Structures (hereafter "CSA")3.
This paper adds to the growing number of studies using databases to evaluate
code provisions for the shear capacity of reinforced and prestressed concrete
members4,5,6. Similar to previous works, the current paper also elucidates the
conservatism and accuracy of design codes, and identifies conditions for which the codes
may be unconservative. The paper also identifies the bias and coefficient of variation in
i Soltani, M. and Ross, B. E., “Interface Shear Transfer Database for Uncracked Concrete Members,” ACI
Structural Journal, in press, 2016.
7
the codes, values which can be used by other researchers in performing reliability
analyses involving interface shear transfer.
Fig. 1-Interface shear transfer between precast girder and cast-in-place deck
RESEARCH SIGNIFICANCE
The motivation and objective of this paper is to benchmark the accuracy of
current interface shear transfer code provisions and to identify possible unconservative
design scenarios. Technical contributions are threefold. First, this paper presents and
documents a newly created database of interface shear transfer experiments in uncracked
concrete members. Second, this paper evaluates the overall conservatism and accuracy of
each of the three mentioned codes. Finally, this paper evaluates the relationship of
different variables to the conservatism -or lack thereof- inherent in each code; conditions
that may result in unconservative calculations are identified. The database and analyses
8
will provide a ledge for future research on improving code provisions, and for future
reliability studies of structures utilizing interface shear transfer.
BACKGROUND
Shear friction
In 1960s, the shear friction concept was proposed to explain shear force transfer
across cracks in reinforced concrete members7,8. The concept is based on a saw-tooth
model as shown in Fig. 2a. Shear force causes horizontal displacement, h, between two
concrete surfaces. Because of aggregate interlock the horizontal displacement is
accompanied by vertical displacement, v. Vertical displacement leads to tension in steel
reinforcement crossing the crack; this tension results in a clamping force on the interface.
In shear friction theory, capacity is equal to the clamping force multiplied by a friction
coefficient.
Using the concept described in Fig. 2a, researchers have proposed methods for
calculating shear strength across different types of concrete interfaces such as between
precast and cast-in-place elements, at cold joints, between existing and repaired elements,
and at cracks9,10. These efforts led to shear friction provisions being introduced in 1977
edition of ACI 31811. Shear friction provisions in the 2014 edition of ACI 31812 are
similar to those first introduced in 1977.
Interface shear transfer
The shear friction concept used in ACI 318 is based on force transfer across an
existing or assumed crack. Strength and behavior of initially uncracked specimens differ
from those with preexisting cracks. Tests have shown that uncracked specimens can have
9
approximately 10% to 100% more capacity than similar specimens with preexisting
cracks (e.g. 10,13).
(a) Saw-tooth model (b) Mechanics
Fig. 2- Interface Shear Transfer (after Santos and Julio [35])
In contrast with the shear friction concept, Hsu et al.14 proposed an interface shear
transfer concept based on a truss model, wherein failure occurs by crushing of concrete
struts. Hwang and Gohnert proposed similar models and applied them to both cracked
and uncracked shear planes15,16. In the current paper the term “interface shear transfer” is
used to denote shear transfer across interfaces that are not initially cracked. An example
of an uncracked interface would be the aforementioned connection between precast
girders and cast-in-place composite bridge decks.
Shear friction is one of three different mechanisms that transfer shear forces
across uncracked interfaces in reinforced concrete members. The mechanisms include: 1)
shear friction (as previously explained), 2) cohesion between concrete surfaces across the
interface, and 3) dowel action from reinforcement that crosses the interface17,18. The
relative contributions of these components vary based on the magnitude of the applied
10
shear force and the degree of slip displacement occurring between the interfaces (Fig.
2b)17,18. At low load levels the shear force is resisted almost exclusively through
cohesion. At higher loads cracks form at the interface, cohesion is broken, and forces are
carried through a combination of shear-friction and dowel action.
The interface shear transfer concept is the basis of provisions in LRFD, EC, and
CSA. These codes consider the contributions from cohesion and friction; contributions
from dowel action are not explicitly considered. Details of the codes are provided later in
the paper.
Previous database studies
Mattock19 created a database of 192 pre-cracked specimens from 10 experimental
studies. Specimens were categorized according to unit weight of concrete, load type
(cyclic, sustained, and static), and interface roughness. It was concluded that the shear
friction provisions of ACI 318-9920 unnecessarily limited the benefits of high strength
concrete. Equations were proposed for determining an upper-limit shear friction
capacity; application of these equations allows the beneficial effects of high strength
concrete on shear friction capacity to be realized. These equations were included in the
200221 and subsequent editions of the ACI 318 code.
A database of 537 tests were collected by Lang22 to evaluate the LRFD interface
shear transfer provisions. The study focused on concrete weight and interface surface
treatments. Results indicated that the reliability index for the LRFD interface shear
provisions is lower than the desired target reliability index of 3.5. The reliability index is
a measure of the likelihood of a failure; higher reliability indexes denote less probability
11
of failure. Lang concluded that improved equations are needed for calculating interface
shear capacity. The study considered both pre-cracked and uncracked specimens and did
not consider the minimum interface reinforcement provisions from LRFD. The current
paper is distinct from Lang’s work in that it includes updated test data, focuses
exclusively on uncracked reinforced specimens, considers LRFD minimum
reinforcement requirements, and includes evaluations of EC and CSA.
To investigate interface shear transfer in lightweight concrete, Sneed and Shaw23
created a database of 300 specimens from eight experimental studies. Normal weight,
sand-lightweight, and all-lightweight concretes were considered. The database was
compared to provisions in both the PCI Design Handbook24 and the ACI 318-11 code. It
was concluded that concrete unit weight does not affect shear friction and interface shear
transfer strengths.
CODE PROVISIONS FOR INTERFACE SHEAR TRANSFER
LRFD
Provisions for interface shear strength are contained in section 5.8.4 of LRFD1.
Nominal capacity is based on cohesion between the interface surfaces and by friction that
results from reinforcement crossing the interface.
The nominal interface shear resistance (Eq. 5.8.4.1-3) is given by:
(1)
where c is the cohesion factor, is the area of concrete considered to be engaged in
interface shear transfer, is the friction factor, is the area of interface shear
12
reinforcement crossing the shear plane within the area , is the yield stress of
reinforcement but design value not exceed 414 MPa (60 ksi), and is the permanent net
compressive force normal to the shear plane.
The nominal interface shear resistance calculated by Equation (1) is limited to the
lesser of:
(2)
(3)
where is the fraction of concrete strength available to resist interface shear, is the
specified 28-day compressive strength of the weaker concrete on either side of the
interface and is the limiting interface shear resistance. Specified compressive strength
must be greater than 16.55 MPa (2.4 ksi). The resistance factor for shear ( ) is 0.8 for
lightweight concrete and 0.9 for normal weight concrete.
The factors c, , , and are presented in LRFD Section 5.8.4.3 and are listed
in Table 1. According to the commentary in LRFD, these values were derived from
multiple experimental studies9,13,19,25,26,27,28.
13
Table 1-Factors for LRFD
Condition c (ksi) μ K1 K2 (ksi)
Cast-in-place concrete slab on clean concrete girder
surfaces, free of laitance, surface roughened to an
amplitude of 6 mm
0.28 1 0.3
1.8 NWC
1.3 LWC
Normal-weight concrete placed monolithically 0.4 1.4 0.25 1.5
Lightweight concrete placed monolithically, or non-
monolithically, against a clean concrete surface, free of
laitance, surface roughened to an amplitude of 6 mm
0.24 1 0.25 1
Normal-weight concrete placed against a clean concrete
surface, free of laitance, with surface intentionally
roughened to an amplitude of 6 mm
0.24 1 0.25 1.5
Concrete placed against a clean concrete surface, free of
laitance, but not intentionally roughened 0.075 0.6 0.2 0.8
Concrete anchored to as-rolled structural steel by headed
studs or by reinforcing bars where all steel in contact with
concrete is clean and free of paint 0.025 0.7 0.2 0.8
LRFD requires that a minimum area of reinforcement cross concrete-to-concrete
interfaces. Minimum area of interface reinforcement, , is given as:
(4)
Equation (4) is not dimensionally consistent. The value for must be input in
in2 or cm2, and the value for must be input in ksi or MPa. Units for the resulting value
for minimum reinforcement are then taken as cm2 (if US Customary units are used, in2).
14
EC
Provisions for shear capacity at the interface between concrete cast at different
times is presented in section 6.2.5 of EC2. Shear capacity due to cohesion and friction are
considered. The provisions are stress-based. Shear stress capacity of an interface ( )
is given by:
(5)
where is the design tensile strength of concrete; is the stress per unit area caused
by the minimum external normal force across the interface that can act simultaneously
with the shear force, positive for compression, such that ; is the design
yield strength of reinforcement, not more than 600 MPa (87.02 ksi); is the cross
sectional area of reinforcement; is the area of the interface; is the angle between
concrete interface and interface reinforcement; and is the design value of concrete
compressive strength. and are factors that depend on the roughness of the interface;
values are listed in Table 2. The strength reduction factor, , is given by:
(6)
where is the characteristic compressive cylinder strength (in MPa) of concrete at 28
days in range of 12 MPa (1.74 ksi) to 90 MPa (13.05 ksi).
15
Table 2-Factors for Eurocode
Condition C
Very smooth interface roughness condition; A surface cast against steel,
plastic or specially prepared wooden molds. 0.025 0.5
Smooth interface roughness condition; A slip-formed or extruded
surface, or a free surface left without further treatment after vibration. 0.2 0.6
Rough interface condition; A surface with at least 3 mm roughness at
about 40 mm spacing, achieved by ranking, exposing of aggregate or
other methods giving an equivalent behavior.
0.4 0.7
Indented interface condition; A surface with indentations complying
more than 3 mm roughness and also depth of groove should be more
than 5 mm and width of groove should be more than 10 times of the its
depth.
0.5 0.9
CSA
The interface shear transfer model in CSA3 considers shear resistance by cohesion
and by friction. As with EC, interface shear transfer provisions in CSA are stress-based.
The following equation for interface shear resistance is given in section 11.5:
(7)
where is 1.00 for normal-weight and 0.75 lightweight concrete; area of shear-
friction reinforcement; is the area of concrete section resisting shear transfer; is the
specified yield strength of non-prestressed reinforcement or anchor steel, not more than
500 MPa (72.52 ksi); and is the angle between shear friction reinforcement and shear
plane. The cohesion and friction factors, and , are listed in Table 3. The resistance
factor for concrete, , is 0.65, and the resistance factor for non-prestressed reinforcing
bars, , is 0.85. Minimum compressive strength of concrete allowed by the design code
is 19.99 MPa (2.9 ksi). The compressive stress on the interface, , is calculated as:
16
(8)
where is the unfactored permanent load perpendicular to the shear plane.
Table 3-Factors for CSA
Condition c
(MPa)
For concrete placed against hardened concrete with the surface
clean but not intentionally roughened 0.25 0.6
For concrete placed against hardened concrete with the surface
clean and intentionally roughened to a full amplitude of at least 5
mm
0.5 1
For concrete placed monolithically 1 1.4
For concrete anchored to as-rolled structural steel by headed
studs or by reinforcing bars. 0 0.6
Additional code considerations
LRFD, EC, and CSA are similar in that they each consider interface shear
resistance to be a combination of cohesion and friction components. The factors used to
weight these components, however, are different in each code. For example, cohesion is
assumed to have a greater share of shear resistance in LRFD in comparison to the other
codes (see Tables 1, 2, and 3). Differences are also noted in the friction coefficients
( used in each code.
LRFD requires a minimum amount of shear reinforcement across interfaces
(Equation 4). The other two codes do not contain such a requirement. Limits on material
properties are also different for each code. The maximum reinforcement yield strength
for design is 414 MPa (60 ksi), 600 MPa (87.02 ksi), and 500 MPa (72.52 ksi) for LRFD,
EC, and CSA, respectively. Additionally, minimum allowed concrete compressive
17
strength for LRFD, EC, CSA are 16.55 MPa (2.4 ksi), 12 MPa (1.74 ksi), and 19.99 MPa
(2.9 ksi), respectively.
Treatment of strength reduction factors is different in each code. LRFD uses a
single reduction factor based on concrete unit weight. EC has a safety factor applied
within the design tensile strength of concrete ( ) and a reduction factor that is also
applied within the maximum limit allowed for interface shear stress (see Equation 5).
CSA has separate reduction factors for the concrete and reinforcement contributions (see
Equation 7).
INTERFACE SHEAR TRANSFER DATABASE
Data from experimental tests of reinforced concrete specimens with uncracked
interfaces were gathered through a literature search. A total of 774 specimens from 25
references were reviewed. Among them 220, 311, and 383 tests were identified for use in
evaluating LRFD, EC, and CSA, respectively. Details of the individual specimens are
listed in the Appendix. The filtering process used to identify applicable data for each
code is discussed below.
Filtering Processes
The filtering process was conducted in two stages. The first phase excluded
specimens that are not relevant to interface shear transfer. The second phase was used to
create code-specific databases for LRFD, EC, and CSA. In this manner each code was
evaluated using specimens that are consistent with its unique requirements. For example,
the LRFD database only included specimens that satisfy the minimum reinforcement
limit; EC and CSA have no such limit and their databases include specimens without
18
reinforcement. Because each code is evaluated using a unique database, comparisons
between codes are not warranted.
The filtering process is diagramed in Fig. 3. In the initial phase of filtering the
primary reason for excluding specimens was that they were pre-cracked. Pre-cracked
specimens are applicable for comparison with design codes such as ACI-318 (2014)12
that are based exclusively on shear-friction and assume a crack has formed at the
interface plane. The aforementioned paper by Mattock19 compared the shear friction
provisions of ACI with a database of pre-cracked specimens.
Fig. 3- Filtering process of the database
Type of test method was also a common reason for exclusion; only those methods
relevant to interface shear design provisions were included. Test methods used in the
19
referenced papers are shown in Fig. 4. Splitting tests were excluded because they do not
create shear forces along an interface; corbel tests because they induce both shear and
moment; and pull-off tests because they rely on reinforcement parallel and near the
interface to transfer tensile forces to the concrete. Push-off, incline shear, and beam
specimens were included in the database. Other reasons for exclusion included failure
modes other than interface shear failure, unidentified interface roughness condition, and
presence of grout at the interface. The initial filtering process reduced the number of
specimens to 428.
(a) Splitting (b) Corbel with moment (c) Pull-off
(a) Push-off (e) Slant-shear (f) Beam
Fig. 4-Test methods
20
For the LRFD database, the secondary filtering removed 178 specimens that had
less than minimum reinforcement (Equation 4), and 30 specimens with compressive
strength lower than the 16.6 MPa (2.4 ksi) limit. The final database for LRFD had a total
of 220 specimens.
In EC monolithic concrete is not included as a part of interface shear transfer.
Accordingly, 76 monolithic specimens were removed from the EC database during
secondary filtering. Also, 43 specimens with compressive strength lower than 12 MPa
(1.74 ksi) were removed. The final database for EC had 311 specimens.
For the CSA database, the secondary filtering removed 45 specimens with compressive
strengths lower than 20 MPa (2.9 ksi). The final database for CSA had a total of 383
specimens.
Code-Specific Database Characteristics
The average compressive strength of concrete ( ) for LRFD, EC, and CSA code-
specific databases were 34.1 MPa (6.25 ksi), 37.83 MPa (5.48 ksi), and 39.38 MPa (5.71
ksi), respectively. Moreover, the average area of concrete interface ( ) for LRFD, EC,
and CSA code-specific databases were 776.30 cm2 (120.36 in2), 921.82 cm2 (142.92 in2),
and 908.04 cm2 (140.78 in2), respectively. Finally, the average interface reinforcement
index ( ) for LRFD, EC, and CSA code-specific databases were 44.49 MPa (6.45 ksi),
38.45 MPa (5.58 ksi), and 42.80 MPa (6.21 ksi), respectively. In cases where different
concretes were used in the same specimen, the lower strength was recorded in the
database. In the database, compressive strength of concrete is calculated based on
uniaxial compressive strength of cylinder specimens. In cases where cube strengths are
21
reported, they were converted to cylinder strengths using relations in EC2. The
reinforcement index provides a measure of the amount and strength of reinforcement
crossing the interface, where is defined as:
(9)
Table 4 presents details of the final databases for each code including interface
roughness condition, concrete weight, test method, and failure mode. In some cases,
specimens had normal weight and lightweight concrete on opposite sides of the interface.
Such specimens were considered lightweight in Table 4 and in the code comparisons.
Table 4- Distributions of experimental variables in code-specific databases
Parameters LRFD
(220 tests), %
EC
(311 tests), %
CSA
(383 tests), %
Concrete
weight
LWC 32 18 23
NWC 68 82 77
Interface
condition
Monolithic 29 0 19
Smooth 22 20 16
Roughened<6mm 0* 27 33
Roughened≥6mm 49 53 32
Failure
mode
Interface 40 73 64
Substrate 41 27 36
Not specified 19 0 0
Test type Push-off 88 61 89
Beam 9 37 2
Slant-shear 3 2 9
*Per section 5.8.4.3 of LRFD, roughness amplitudes less than 6mm are considered as
smooth.
EVALUATION OF CODES
The experimental-to-nominal interface shear capacity ratio (hereafter ‘strength
ratio’), , was calculated for each specimen in the final database to evaluate the
22
conservatism of each design code. The average strength ratio is the bias between the
nominal and experimental capacities. Values of strength ratio greater than 1.0 indicate
that the code-calculated capacity is conservative relative to the experimental capacity.
The coefficient of variation (COV) of the strength ratios was also calculated for each
code. COV provides a measure of how consistently a given code produces a level of
conservatism. As the degree of consistency increases, the COV decreases.
To provide a frame of reference for evaluating the interface shear transfer code
provisions it is helpful to consider strength ratio and COV for other shear provisions in
the building codes. The rationale for this comparison is that interface shear capacity
calculations should provide a similar level of conservatism as other code-based nominal
shear strengths. Strength ratios (bias factors) for shear capacity of prestressed beams
have been reported as 1.14 to 1.30 with COV of 0.14 to 0.2029,30,31,32,33. Thus the interface
shear transfer provisions of LRFD, EC, and CSA are more conservative than prestressed
beam shear capacity calculations when they have strength ratios greater than 1.30, and
are less consistent when they have COV greater than 0.20. Additionally, the NCHRP
Report #733, using the shear transfer provision of LRFD, reported the bias factor of 1.27
and 1.16 with COV of 0.23 and 0.19 for light weight and normal weight concretes,
respectively34.
Nominal capacities were calculated using the tested yield strength of
reinforcement up until the code-based upper limits. Tested concrete strengths were used
in the calculations. Capacities with and without strength reduction factors were
calculated.
23
Each design code was assessed based on its own unique database, wherein all
specimens satisfied the specific requirements of the given code. Thus, results from the
different codes are not compared to each other.
Overall Evaluation
Results of the code evaluations are summarized in Table 5 and Fig. 5. In general,
the interface shear transfer provisions of LRFD, EC, and CSA are more conservative than
code provisions for beam shear, which is desirable, because they also produce less
consistent levels of conservatism than the beam shear provisions. Overall observations of
the individual codes are discussed below.
LRFD: The average strength ratio of LRFD was 1.49 and the COV of the
strength ratio was 0.38. Although not as consistent as beam-shear provisions, the LRFD
code produced relatively consistent levels of conservatism across the LRFD database.
This result can also be qualitatively observed in the histograms shown in Fig. 5, wherein
strength ratios for LRFD have a relatively tight distribution around the mean.
Unconservative results occurred in 18 out of 220, or 8.2% of tests.
(a) LRFD (220 tests) (b) EC (311 tests) (c) CSA (383 tests)
Fig. 5-Distributions of interface shear transfer strength ratio
24
Table 5-Summary of code comparisons
(a) No reduction factor applied
LRFD EC CSA
Number of tests 220 311 383
Minimum strength ratio 0.59 0.62 0.55
Maximum strength ratio 3.87 4.54 21.7
Mean strength ratio 1.49 1.93 2.83
Strength ratio standard deviation 0.57 0.71 2.28
Strength ratio COV 0.38 0.37 0.80
Unconservative cases 18 16 29
Unconservative % 8.2% 5.1% 7.6%
(b) Reduction factor of design codes applied
LRFD EC CSA
Number of tests 220 311 383
Minimum strength ratio 0.74 0.66 0.56
Maximum strength ratio 4.40 6.81 21.7
Mean strength ratio 1.85 2.49 4.00
Strength ratio standard deviation 0.67 1.07 3.54
Strength ratio COV 0.36 0.43 0.88
Unconservative cases 4 5 9
Unconservative % 1.8% 1.6% 2.3%
The results presented in Table 5 (b) are based on calculations using strength
reduction (i.e. resistance) factors. These results are useful for comparing the design
strength, which engineers calculate in practice. For LRFD, the strength reduction factors
resulted in a strength ratio of 1.85 and a COV of 0.36. Unconservative cases reduced to 4
cases, or 1.8% of the database.
EC: The average strength ratio of EC was 1.93, with a COV of 0.37.
Unconservative cases occurred in 16 out of 311 tests (5.1%). Minimum and maximum
strength ratios from the EC analyses were 0.62 and 4.54, respectively. When considering
25
the safety factor that is applied to the design tensile strength of concrete and the reduction
factor in the maximum limit for interface shear stress, the average strength ratio increased
to 2.49, with only five (1.6%) specimens having unconservative capacities.
CSA: The average strength ratio and COV of CSA were 2.83 and 0.80,
respectively. The relatively high COV indicates that conservatism of the CSA code was
inconsistent for the experimental data. Unconservative cases were observed in 29 out of
383 tests (7.6%). Applying CSA resistance factors to the calculated strengths, average
strength ratio was 4.0 and COV was 0.88. Unconservative results occurred in only 9
cases (2.3%) when the resistance factors were included in the analysis.
Detailed Evaluation
Fig. 6 presents the strength ratios for each code relative to different experimental
variables. Dashed lines in the figure are moving averages of the strength ratio. The
moving average gives an indication of the degree to which conservatism changes across
the range of a given variable. A flat line occurs when conservatism is consistent across
the range of values; steep lines occur when the degree of conservatism differs. For the
discussion presented in this paper, the degree of conservatism is based on the strength
ratio, with higher ratios indicating greater conservatism.
A bin analysis was also used to evaluate relationships between strength ratio and
specimen variables. The range of each variable was divided into four equally-spaced bins.
Table 6 reports the average strength ratio, COV, number of tests, number of
unconservative tests, and unconservative percentage for each bin. The bin analysis and
26
moving averages shown in Fig. 6 are based on the strength ratio without strength
reduction factors.
The effects of concrete unit weight and interface surface condition were also
studied, with the results shown using box-and-whiskers plots in Fig. 7. Data presented in
Fig. 7 does not consider the strength reduction factors.
LRFD: Referring to the moving average line in Fig. 6 it can be seen that LRFD
produced varying levels of conservatism across the range of concrete strengths in the
experimental data. Lower concrete strengths related to lower average strength ratios. This
can also be observed from the bin analysis, wherein the average strength ratio of concrete
compressive strength between 30 MPa (4.3 ksi) to 60 MPa (8.6 ksi) is 1.41, and 11% of
the specimens in the bin had unconservative results.
Both the moving average and the bin analysis suggest a slight downward trend in
conservatism as the interface area increases. The average strength ratio for the bin with
the smallest specimens (<750 cm2) was 1.57, whereas the strength ratio was 1.24 for the
bin with the largest specimens (>2250 cm2). This trend, however, is much less
pronounced than the trend observed for the compressive strength. No obvious trends are
noted with regard to reinforcement index.
27
(a) LRFD (220 tests) (b) EC (311 tests) (c) CSA (383 tests)
Fig. 6-Interface shear transfer strength ratios compared to experimental variables
28
Table 6- Bin evaluation of experimental variables
(a) LRFD
parameter , MPa (ksi) , MPa (ksi) , cm2 (in2) <30
(4.3)
30
(4.3)-
60 (8.6)
60
(8.6)-
90 (13.0)
>90
(13.0)
<3
(0.4)
3 (0.4)-
6 (0.8)
6 (0.8)-
9 (1.2)
>9
(1.2)
<750
(116)
750
(116)-
1500 (232)
1500
(232)-
2250 (348)
>2250
(348)
Average
Strength
ratio
1.29 1.41 2.51 1.65 1.53 1.50 1.41 1.62 1.57 1.44 1.29 1.24
COV 0.23 0.34 0.27 0.05 0.33 0.48 0.32 0.42 0.41 0.31 0.33 0.23
Tests 74 113 23 10 78 60 66 16 134 60 7 19
Uncons.
Tests
6 12 0 0 5 10 2 1 7 6 2 3
Uncons.
%
8.1 11 0.0 0.0 6.4 17 3.0 6.2 5.2 10 29 16
(b) EC
parameter , MPa (ksi) , MPa (ksi) , cm2 (in2) <30
(4.3)
30
(4.3)-
60 (8.6)
60
(8.6)-
90 (13.0)
>90
(13.0)
<3
(0.4)
3 (0.4)-
6 (0.8)
6 (0.8)-
9 (1.2)
>9
(1.2)
>750
(116)
750
(116)-
1500 (232)
1500
(232)-
2250 (348)
>2250
(348)
Average
Strength
ratio
2.16 1.67 2.30 - 2.15 1.66 1.37 1.24 1.89 2.02 1.79 1.72
COV 0.79 0.55 0.61 - 0.67 0.67 0.38 0.64 0.63 0.81 0.45 0.44
Tests 36.3
7
32.72 26.51 0 30.9
0
40.40 27.68 51.8
4
33.41 39.95 25.35 25.86
Uncons.
Tests
129 153 29 0 211 39 50 11 115 153 15 28
Uncons.
%
4 10 2 - 3 4 4 5 4 11 1 0
(c) CSA
parameter , MPa (ksi) , MPa (ksi) , cm2 (in2) <30 (4.3)
30 (4.3)-
60
(8.6)
60 (8.6)-
90
(13.0)
>90(13.0)
<3 (0.4)
3 (0.4)-6 (0.8)
6 (0.8)-9 (1.2)
>9(1.2)
>750 (116)
750 (116)-
1500
(232)
1500 (232)-
2250
(348)
>2250(348)
Average
Strength
ratio
3.14 2.28 3.05 5.32 3.74 1.51 1.19 0.95 2.14 3.38 2.59 3.77
COV 0.88 0.72 0.46 0.19 0.65 0.25 0.19 0.32 1.25 0.50 0.27 0.59
Tests 174 164 33 12 241 60 66 16 170 172 13 28
Uncons.
Tests
13 16 0 0 0 7 11 11 21 8 0 0
Uncons.
%
7.5 9.8 0.0 0.0 0.0 12 7 69 12 4.7 0.0 0.0
29
Fig. 7 shows distribution of strength ratios based on concrete weight and interface
roughness condition. Differences in average strength ratio based on concrete unit weight
are within the scatter of the data. The data shown in Fig. 7 are based on the different
factors proscribed in LRFD for light weight and normal weight concretes. Because of the
consistent strength ratios, it appears that LRFD adequately accounts for any effects of
concrete unit weight. For LRFD, smooth interfaces resulted in more conservative
capacities relative to monolithic and roughened surfaces (R≥6mm). The latter two have
approximately the same level of conservativism.
EC: Conservatism of the EC code varied across each of the variables presented in
Fig. 6. The only variable with a clear trend, however, was for the reinforcement index;
the strength ratio of EC was inversely related to the reinforcement index. Unreinforced
specimens had an average strength ratio of 2.59. The difference between unreinforced
and reinforced specimens accounts for the abrupt increase in average strength ratio as the
index approaches zero. The average strength ratio for reinforced specimens was 1.75,
with more heavily reinforced specimens resulting in smaller strength ratios (i.e. less
conservatism).
Referring to Fig. 7 it can be observed that the average strength ratio of light-weight
concrete specimens is higher than the ratio for normal weight; however the difference
was within the scatter of the data. In contrast to LRFD and CSA, EC does not treat for
light-weight concrete differently when calculating interface shear capacity. Fig. 7 also
shows that specimens having surfaces that are roughened to amplitudes of 6mm or less
resulted in larger degrees of conservatism than did other interface conditions.
30
(a) LRFD (220 tests) (b) EC (311 tests) (c) CSA (383 tests)
Fig. 7-Interface shear transfer strength ratios compared to concrete unit weight and
surface roughness. Boxes indicate the upper and lower quartile of scatter, whiskers
indicate the range.
CSA: Based on the results presented in Fig. 6, conservatism of the CSA code varies
with changes to each of the considered variables. In general conservatism goes up with
larger interface area, down with greater amounts of interface reinforcement, and up with
increasing concrete strength.
Perhaps the most alarming result from the entire study is the unconservative strength
ratio for CSA for specimens with large amounts of interface reinforcement. This can be
observed from the bin analysis, wherein heavily reinforced specimens with > 9 MPa
had an average strength ratio of 0.95. The same bin had the highest incident of
31
unconservative results in the entire study, with 11 of the 16 specimens (69%) failing to
reach the CSA-based nominal interface shear transfer capacity. These results suggest the
need for caution on the part of engineers using the CSA code to design heavily reinforced
concrete interfaces. Additional testing is recommended to elucidate this result and to
determine if the CSA code should be modified to provide an increased safety margin for
interface shear transfer in heavily reinforced members.
As with EC, the CSA code resulted in higher levels of conservatism for unreinforced
specimens. The average strength ratio for CSA was 4.48 for unreinforced specimens and
2.39 for reinforced specimens. No unconservative results were observed for unreinforced
or lightly ( < 3 MPa) reinforced specimens.
While not as definitive as the relationship with reinforcement index, the analyses
suggest that the concrete compressive strength and interface size are also correlated with
the strength ratio of CSA. Smaller compressive strengths and interface areas correspond
to lower degrees of conservatism. The bin analysis hints at these relationships, wherein
unconservative results only occurred in the bins with specimens having concrete
compressive strength less than 60 MPa and interface areas less than 1500 cm2.
From Fig. 7 it is observed that the CSA code resulted in larger degrees of conservatism
for specimens having surfaces that are roughened to amplitudes up to 6mm. The degree
of conservatism is relatively consistent for monolithic, smooth, and roughened >6mm
interfaces.
SUMMARY AND CONCLUSIONS
32
A database of interface shear transfer tests was compiled from the existing
literature, and was used to evaluate accuracy of models from three codes: AASHTO
LRFD 2014, Eurocode 2 2004, and CSA A23.3-14 2014. The evaluations focused on
specimens that did not have cracks (uncraked) prior to testing. This condition is similar to
uncracked cold-joints between attached elements, such as at deck-to-girder interfaces.
The overall database was filtered in order to create code-specific databases for LFRD,
EC, and CSA. For example, specimens without interface reinforcement were removed
from the LRFD database because of the minimum reinforcement requirements in LRFD.
Because a unique database was used for each code, the subsequent evaluations are useful
for comparing the codes against test data, but are not used to compare between codes. In
general, the code-calculated nominal capacities were conservative relative to the
experimental data. Key conclusions and observations from the code-specific evaluations
are as follows:
LRFD
When strength reduction factors were not included in the analyses, the
average experimental-to-nominal strength ratio for LRFD was 1.49 and the
coefficient of variation was 0.38. Unconservative results (experimental
capacity less than calculated nominal capacity) were observed in 18 of 220
(8.2%) specimens.
When the strength reduction factor was applied in the analyses,
unconservative results occurred in only 4 of 220 (1.8%) specimens. The
average experimental-to-nominal strength ratio was 1.85.
33
As compressive strength decreased, the degree of conservatism also
decreased. The average strength ratio of specimens having compressive
strength less than 30 MPa was 1.24, and individual unconservative results
were only observed when the concrete compressive strength was lower than
60 MPa (8.6 ksi).
EC
The average experimental-to-nominal strength ratio and COV were 1.93 and
0.37, respectively, when strength reduction factors were not considered.
When the strength reduction factor was considered the strength ratio
increased to 2.49, but the number of unconservative results did not change.
Five of 311 (1.6%) specimens were unconservative in both cases.
Conservatism of the EC code is inversely related to the interface
reinforcement index (a measure of the strength and amount of interface
reinforcement). Presence or lack of reinforcement was also significant; the
average strength ratio was 2.59 for unreinforced specimens and 1.75 for
reinforced specimens.
CSA
The average experimental-to-nominal strength ratio and COV for the CSA
were 2.83 and 0.80, respectively, when strength reduction factors were not
considered. Out of 383 specimens, 29 (7.6%) demonstrated less than nominal
capacity.
34
Applying strength reduction factors, the average experimental-to-nominal
strength ratio and COV were 4.00 and 0.88, respectively. Unconservative
cases were 9 (2.3%).
The most alarming observation is the relationship between reinforcement
index and conservatism of CSA. Eleven (69%) of the 15 specimens having a
reinforcement index greater than 9 MPa failed at loads lower than the CSA-
calculated nominal value. The average strength ratio of these specimens was
0.95. Additional studies are recommended to add data and insights regarding
this potentially unsafe condition.
NOTATION
= Area of concrete interface in AASHTO LRFD 2014 and CSA A23.3-14 (cm2)
= Area of concrete interface in Eurocode 2 (cm2)
= Area of interface reinforcement in AASHTO LRFD 2014 and CSA A23.3-14 (cm2)
= Area of interface reinforcement in Eurocode 2 (cm2)
= Width of interface concrete cross-section (cm)
= Characteristic compressive cylinder strength of concrete at 28 days in Eurocode 2
(MPa)
= Specified compressive strength of concrete in AASHTO LRFD 2014 and CSA
A23.3-14 (MPa)
= Design value of concrete compressive strength in Eurocode 2 (MPa)
= Yield strength of reinforcement in AASHTO LRFD 2014 and CSA A23.3-14 (MPa)
35
= Design yield strength of reinforcement in Eurocode 2 (MPa)
= Fraction of concrete strength available to resist interface shear in AASHTO LRFD
2014
= Limiting interface shear resistance in AASHTO LRFD 2014 (MPa)
= Length of interface concrete cross-section (cm)
= Un-factored permanent load perpendicular to the shear plane in Eurocode 2 (kN)
= Permanent net compressive force normal to the shear plane in AASHTO LRFD 2014
(kN)
= Nominal shear resistance of interface shear transfer in Eurocode 2 (MPa)
= Nominal shear resistance of interface shear transfer in CSA A23.3-14 (MPa)
= Nominal shear resistance of interface shear transfer in AASHTO LRFD 2014 (kN)
= Nominal interface shear transfer strength calculated from codes (kN)
= Ultimate experimental interface shear transfer (kN)
= Angle between shear reinforcement and interface in CSA A23.3-14
= Angle between shear reinforcement and interface in Eurocode 2
= Compressive stress in CSA A23.3-14 (MPa)
= Concrete weight factor
= Strength reduction factor in Eurocode 2
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36
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38
[22] Lang, M., “Analysis of the Aashto LRFD Horizontal Shear Strength Equation,”
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[32] Nowak, A. S., Park, C.-H., and Casas, J. R., “Reliability analysis of prestressed
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[35] Santos, P. M. D., and Júlio, E. N. B. S., “A state-of-the-art review on shear-friction,”
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[36] Shaw, D. M., and Sneed, L. H., “Interface shear transfer of lightweight-aggregate
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SHEAR FRICTION APPLICATIONS,” University of Pittsburgh, 2009.
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42
CHAPTER THREE
A STATISTICAL APPROACH TO REFINE DESIGN CODES FOR INTERFACE
SHEAR TRANSFER IN REINFORCED CONCRETE STRUCTURESi
Introduction
Many Reinforced Concrete (RC) structures depend on transfer of shear forces
across concrete-to-concrete interfaces. The Interface Shear Transfer (hereafter referred to
as “IST”) theory describes the mechanisms by which shear forces are transferred across
RC interfaces. The connection of precast concrete girders and cast-in-place concrete
bridge decks is a common example of the IST (Fig. 1). Bridge stiffness and strength
depend on the composite action between the girder and deck, which action requires
interface transfer of shear forces.
Fig. 1- Interface shear transfer between precast girder and cast-in-place deck
i Soltani, M., Ross, B. E., & Khademi, A., “A Statistical Approach to Refine Design Codes for Interface
Shear Transfer in Reinforced Concrete Structures,” submitted (under review), 2016.
43
Previous research by Soltani and Ross1 has demonstrated that current code-based
IST models produce inconsistent levels of accuracy. For example, accuracy of the
AASHTO LRFD 20142 (Hereafter referred to as “LRFD”) IST model varies significantly
for different compressive strengths of concrete. When compared to experimental data,
LRFD model resulted in an average factor of safety of 1.29 for specimens with
compressive strength of concrete less than 30 MPa (4.3 ksi). In contrast, the average
factor of safety was 2.25 for specimens with compressive strength greater than 60 MPa
(8.6 ksi).
Recognizing the limitations of current code-based IST design models, the current
paper has two objectives. First, this paper presents a sensitivity analysis, which identifies
parameters having the greatest impact on the IST capacity. The sensitivity analysis is
based on Artificial Neural Networks (ANN) models, that were developed using a
previously compiled database1. ANN was chosen for the sensitivity analysis because of
the method’s demonstrated accuracy for evaluating experimental data from tests of
reinforced concrete structures3,4. Second, a multiple linear-regression analysis was used
to create a new design model for IST capacity. The proposed IST model was created to
produce consistent levels of accuracy throughout the considered range of design
parameters. By using a multiple linear-regression approach, the model was formulated in
a manner that it can be readily applied by structural designers. Thus, this paper elucidates
the relative importance of different design parameters on IST capacity and also proposes
a new model that improves upon the primary limitation (inconsistent accuracy) of current
code models.
44
Background
Interface Shear Transfer
Shear forces are carried across concrete-to-concrete interfaces through three
mechanisms including: 1) shear-friction, 2) cohesion between concrete surfaces, and 3)
dowel action of reinforcement5,6. The shear-friction concept was initially proposed by
Mast7 and Birkeland and Birkeland8 to explain shear force transfer across cracks in RC
members. Shear-friction can be explained using a saw-tooth model5 as illustrated in Fig.
2. Shear force causes horizontal displacement, h, between two concrete surfaces. The
horizontal displacement is accompanied by vertical displacement, v, due to concrete
interlock. Vertical displacement causes tension in steel reinforcement crossing the
interface; this tension results in a clamping force and friction along the interface.
Cohesion is the bond between concrete interface surfaces. Dowel action is due to the
direct shear resistance of the reinforcement crossing the interface. When load is small
shear force is resisted almost exclusively through cohesion. However, at higher loads
cracks form as cohesion is broken, and forces are carried through a combination of shear-
friction and dowel action5.
IST in Design Codes and Research Motivation
Current design codes such as LRFD 2014, Eurocode 2: Design of concrete
Structures 20049 (Hereafter referred to as “EC”), and Canadian Standard Association
201410 (Hereafter referred to as “CSA”) contain provisions for calculating IST capacity.
Although IST provisions in each of these codes have some unique features (such as the
values given for the coefficients), the general form of their IST models is similar:
45
Equation 1
where is the nominal IST strength of the concrete member; c is the cohesion factor;
is the area of concrete considered to be engaged in interface shear transfer; is the
friction factor; is the area of interface shear reinforcement crossing the shear plane
within the area ; is the yield stress of reinforcement; and is the permanent net
compressive force normal to the shear plane. Thus, the codes consider IST capacity to be
the summation of cohesion and friction. Contributions from dowel action are not
explicitly considered.
Fig. 2-Interface Shear Transfer, saw-tooth model (after Santos and Júlio 20125)
The effects of concrete strength are of interest in this study. Each of the
considered codes (LRFD, EC, and CSA) use compressive strength of concrete for
calculating upper-bound IST capacity; higher compressive strength leads to increased
values for the upper bound. The EC code also considers concrete tensile strength when
calculating the contribution of cohesion to IST capacity. Each of these codes also have a
46
minimum compressive strength for structural concrete. Thus, the codes indirectly
consider compressive strength of concrete when determining IST capacity.
In a previous study by the authors (Soltani and Ross1), a database of IST tests was
compiled and then used to evaluate the accuracy and conservatism of the LRFD, EC, and
CSA codes. It was reported that the average experimental-to-nominal IST capacity ratio
(hereafter referred to as “strength ratio”), , was 1.49, 1.93, and 2.83 for the LRFD,
EC, and CSA, respectively. The previous study also determined that the accuracy of the
IST models in the codes varies for different values of the design parameters. As
mentioned above, accuracy of the LRFD model varies as a function of concrete
compressive strength. These results were the primary motivations for the current paper.
To what degree does concrete strength affect IST capacity? How can concrete strength be
directly considered when calculating IST capacity? Can a model be developed that
produces a consistent degree of conservatism for different values of design parameters?
Artificial Neural Network and Regression Modeling
Artificial Neural Network (hereafter referred to as “ANN”) are a class of artificial
intelligence models that operate in a manner analogous to that of biological nervous
systems11,12. As a strong computational tools, ANN models are capable of ‘learning’ from
data to identify patterns, categorize data, and predict relationships between inputs and
outcomes. The behavior of an ANN system is governed by connections between
individual computing components, called neurons, and by the weights or strengths of
those connections13. In an ANN, information is transmitted from the input layer to
47
neurons contained within the so-called hidden layers, and eventually to an output layer.
The quality and accuracy of the model training is influenced in part by the selection of
hidden layer quantity14,15,16.
Essentially, an ANN is sophisticated regression model, and is typically more
accurate and flexible than traditional regression methods17. However, one downside of
ANN models is that they are “black boxes” which do not allow direct observation of the
mathematical formulation in the model. In contrast, traditional regression models, such
as multiple linear regression, can be used to create observable mathematical functions.
Because of the strengths and limitations of theses modeling approaches, this paper uses
different approaches to address different research questions. The sensitivity analysis was
conducted using the more accurate ANN approach. To facilitate the creation of practical
design equations, the multiple linear regression approach was used for developing the
proposed model.
ANN Applied to Concrete
ANN models have been used increasingly in different areas of science, including
civil engineering18. With regard to concrete, ANN models have been used successfully
for predicting shear strength for RC beams19,3,20,21, compressive strength of concrete
mixes (e.g. 4 and 22), and other characteristics of concrete mix designs23,24,25. These
studies demonstrate that ANN can be effectively applied to complex problems in concrete
materials and structures, particularly those with multiple interacting variables.
Interface Shear Transfer Database
48
A database of IST experiments complied by Soltani and Ross1 was used in the
current study. The database is comprised of 354 tests of IST capacity on non-monolithic
RC specimens. Because concrete unit weight is of interest in the current study, the
database was split into 256 tests with normal-weight concrete (NWC) and 98 tests with
light-weight concrete (LWC). The 98 LWC specimens include those built completely of
LWC and also specimens with built with both LWC and NWC. Parameters in the
database included, peak experimental capacity ( ), compressive strength of concrete
( ), area of concrete interface ( ), interface shear reinforcement index ( , applied
normal stress ( ), and roughness amplitude of interface ( ). In cases where two different
strengths of concrete were used in one specimen, the smaller compressive strength was
retained in the database.
The interface shear reinforcement index, , provides a measure of the amount
and strength of reinforcement crossing the interface, where is defined as:
Equation 2
The applied normal stress is given by:
Equation 3
Details of the database including minimum value, maximum value, average,
standard deviation, and midrange of input parameters are summarized in Table 1. A more
detailed discussion of the database, including database values and references, is available
in the aforementioned paper (Soltani and Ross 2016).
Evaluation Using Artificial Neural Network
49
Methodology – ANN Model
The MATLAB Neural Network Toolbox (MATLAB 2014)26 was used to create
the ANN models. Two models were built, one for specimens with NWC and one for
specimens with LWC. To begin, the source data for each model were randomly selected
so that 70% were used for ANN training, 15% for testing, and 15% for validation. The
70% training set was used to develop and train a network, which was initially compared
to the 15% testing set. The training and testing processes were repeated to seek a well-
fitted solution. Once a solution was identified, the validation set was used to measure
network generalization and to stop training when generalization stops improving. The
testing set had no influence on training, but provided an independent measure of network
performance after training. All training, testing, and validation operations were
automated within MATLAB.
The ANN models in this study were developed having five input parameters ( ,
, , , and ), ten hidden layers (Fig. 3), and one output parameter ( ). These
input parameters were chosen because they represent the variables considered in current
code-based IST models. The input-output and curve fitting algorithm from the MATLAB
ANN toolbox was used as the training algorithm. Once the ANN models were created
and validated, sensitivity analyses were performed using a one-factor-at-a-time process.
The ANN models were used to estimate IST strength for each different level of the
variable, and the process was repeated for each input parameter. The basepoint used in
the sensitivity analyses was taken as midrange of the input parameters (Table 1). Because
50
the NWC and LWC datasets have different ranges, basepoints were different depending
on concrete unit weight.
Table 1- The range of input parameters
NWC
LWC
min Max average St.
Dev.
midrange min max average St.
Dev.
midrange
,
MPa
(ksi)
19.3
(2.8)
106.2
(15.4)
42.0
(6.1)
20.0
(2.9)
62.7
(9.1)
11.7
(1.7)
53.8
(7.8)
31.7
(4.6)
15.2
(2.2)
32.7
(4.75)
,
( )
319.3
(49.5)
3581.3
(555.1)
962.6
(149.2)
497.4
(77.1)
1950.3
(302.3)
169.7
(26.3)
2477.4
(384)
814.8
(126.3)
860.0
(133.3)
1323.5
(205.15)
,
MPa
(ksi)
0
(0)
2.5
(0.37)
0.3
(0.05)
0.5
(0.07)
1.3
(0.18)
0
(0)
1.0
(0.14)
0.3
(0.05)
0.3
(0.05)
0.05
(0.07)
,
MPa
(ksi)
0
(0)
11.7
(1.70)
1.0
(0.14)
2.5
(0.36)
5.9
(0.85)
0
(0)
2.0
(0.29)
0.4
(0.06)
0.5
(0.08)
1.0
(0.14)
,
c
( )
0
(0)
0.6
(0.25)
0.4
(0.14)
0.2
(0.1)
0.3
(0.12)
0
(0)
0.6
(0.25)
0.4
(0.17)
0.3
(0.11)
0.3
(0.12)
Validation
Performance of the ANN models for NWC and LWC are illustrated in Fig. 4. The
ANN-estimated IST strength ( ) for both NWC and LWC were compared to the
experimental IST strengths ( ). For the NWC and the LWC models, the value of
was 0.93 and 0.96, respectively. These values demonstrate a high level of correlation
between the ANN models and experimental data.
51
Fig. 3- Schematic of ANN model
(a) NWC (b) LWC
Fig. 4- ANN performance for the entire database (1 kip= 4.448 kN)
Results and Discussions
52
Sensitivity analyses were performed using the ANN models for NWC and LWC.
The five input parameters were analyzed to determine the degree to which they affect
predicted IST strength, . Results are presented in Fig. 5. The vertical axis in the
figure is the model-predicted capacity divided by the baseline capacity. The horizontal
axis is the normalized input parameter, which is the value of the input variable divided by
the baseline value. For example, the baseline value for compressive strength of concrete
of NWC is 62.7 MPa (9.1 ksi). Thus, a normalized concrete strength of 1.1 corresponds
to a strength of 68.9 MPa (10.0 ksi). Individual curves on the plot are based on a one-
way sensitivity analysis, wherein the factor (parameter) under consideration was varied
and the others were held constant.
(a) NWC (b) LWC
Fig. 5- IST sensitivity analysis using ANN model
Three observations are made from Fig. 5. First, an increase in the input
parameters’ range always resulted in an increase in predicted capacity. Second, the
53
relationships between input parameters and predicted capacity are approximately linear.
This observation suggests that linear models, such as the multiple linear regression model
used later in this paper, could adequately describe the given source data. Third, the
predicted IST strength is most sensitive to the compressive strength of concrete, .
Sensitivity can be determined by comparing the slope of the lines for each parameter.
The line for compressive strength of concrete has the steepest slope for both the NWC
and LWC models, indicating that changes in concrete strength have the greatest impact
on predicted capacity.
Proposed Interface Shear Transfer Model
With the knowledge that each of the five parameters from the sensitivity study
have approximately linear impact on IST capacity, a new design model was developed
based on a multiple linear-regression analysis. As was done with the ANN modeling,
separate linear regression models were built for NWC and LWC. For each model, 80%
of the source data were randomly selected to calibrate the multiple linear-regression
model; the remaining 20% were used to for validation. A spreadsheet was used to
conduct the regression analysis.
Development of the Proposed Model
The proposed IST model is based on the observed behavior from the sensitivity
analyses and on the general form of the current codes (Equation 1). However, in contrast
with the current code IST models, the proposed model directly considers concrete
compressive strength within the cohesion and friction coefficients. Additionally,
54
roughness amplitude is treated as a continuous variable. The proposed model is as
follows:
Equation 4
where is the cohesion coefficient, is the friction coefficient for the shear-friction
mechanism, and is the friction coefficient for the normal force. The coefficients are
taken as functions of and . The physical notion behind this model is that resistance
due to cohesion and friction are based on interface roughness and concrete strength. The
coefficients are defined as:
Equation 5
Equation 6
Equation 7
In expressions mentioned above, unit of , , , , , , and are kN,
cm2, cm2, MPa, kN, and cm in SI system, respectively; similarly, units in US customary
system are kip, in2, in2, ksi, kip, in, and ksi, respectively.
The coefficients to were determined through multiple linear-regression
analysis, and are listed in Table 2. A zero value for a coefficient means the corresponding
input parameter(s) has no influence on the calculated IST strength. Coefficients to
in both datasets are approximately the same. The coefficients associated with normal
force, , are different for NWC and LWC. The Significance-F values determined from
55
multiple linear-regression analysis for NWC and LWC datasets are 8.65E-138 and 4.23E-
62, respectively. The maximum p-values for the non-zero coefficients for NWC and
LWC datasets were 2.86E-07 and 0.000121, respectively. These values indicate that the
linear model describes the data with a desired level of confidence. Because of the value
of these statistical parameters, simple multiple linear regression analysis is deemed
sufficient for this study.
Table 2- Coefficients of the proposed model
Coefficient NWC LWC
SI units
(US customary units)
, MPa
(ksi)
0.4
(0.25)
0.34
(0.22)
0.01
(0.02)
0.02
(0.03)
0
(0)
0
0
10
(3.25)
11
(3.75)
3.8
(0.35)
22
(2.05)
20
(0.65)
0
(0)
Validation
The R2 values for the training and validation databases are presented in Table 3.
The proposed design model has a high level of correlation with the experimental data.
The minimum was 0.88 for training, validation, and total sets of both NWC and LWC.
The multiple linear-regression performance of the total set (training and validation data)
of NWC dataset (256 tests) and LWC dataset (98 tests) are presented graphically in Fig.
56
6. These results demonstrate that the proposed model can describe the data for calculating
IST capacity with a high level of confidence.
(a) NWC (b) LWC
Fig. 6- Multiple linear-regression performance of the proposed model (1 kip= 4.448 kN)
Table 3- Statistical parameters of the regression analysis
Statistical
parameter
NWC LWC NWC and
LWC
Training
(205 tests)
Validation
(51 tests)
Total
(256 tests)
Training
(78 tests)
Validation
(20 tests)
Total
(98 tests)
Total
(354 tests)
Average
strength
ratio
1.09 1.12 1.09 1.05 0.99 1.04 1.08
Standard
deviation
0.32 0.31 0.30 0.21 0.19 0.20 0.29
COV 0.28 0.28 0.27 0.20 0.20 0.19 0.26
0.95 0.88 0.89 0.97 0.92 0.96 0.92
T-tests -assuming two samples with unequal variances- were performed for each
of the NWC and LWC datasets for checking the accuracy of the proposed model when
two populations are considered: tests with and without reinforcement. A t-test is a
57
statistical test used to determine whether two population means are different when the
population variances are unknown and unequal. The t-test results are shown in Table 4.
The t Stat values for the NWC and LWC were -0.17 and 0.92, respectively. Considering
the critical probability values for one-tail and two-tails, the two sample test did not have
different means (Table 4). Thus, the two populations are likely consistent; consequently,
the proposed model is considered applicable for calculating IST capacity in RC structures
with and without reinforcement across the interface.
Table 4- Results of the t-test for with and without reinforcement populations
t-test parameter NWC LWC
With
reinforcement
Without
reinforcement
With
reinforcement
Without
reinforcement
Average strength
ratio
1.09 1.08 1.06 1.00
Variance 0.11 0.03 0.04 0.05
Observations 201 55 73 25
df 159 34
t Stat 0.17 0.92
P(T<=t) one-tail 0.43 0.18
t Critical one-tail 1.65 1.69
P(T<=t) two-tail 0.87 0.36
t Critical two-tail 1.97 2.03
Fig. 7 presents the strength ratios for the proposed model relative to different
experimental variables. Each data point in the figure represents the strength ratio for a
unique test specimen from the database. Dashed lines in the figure are moving average of
the strength ratio, and are based on the average of 20 points. The moving average gives
an indication of the degree to which conservatism and accuracy change across the range
of a given variable. A flat line occurs when accuracy is consistent across the range of
58
values; steep lines occur when the degree of accuracy differs. For all the experimental
variables, the strength ratio of the proposed model hovers at approximately 1.0, which
indicates consistent accuracy over the ranges of variables.
Fig. 7- IST strength ratios compared to experimental variables including NWC and LWC
Comparison with IST Design Codes
59
To evaluate the quality of the proposed model, it is compared with the LRFD,
EC, and CSA codes as shown in Table 5. Comparisons are based on the code-specific
databases reported by (Soltani and Ross 2016). The complete filtering process was
detailed in the previous paper. These databases only include specimens that comply with
the requirements of a given code. For example, LRFD requires a minimum amount of
interface reinforcement, and unreinforced specimens are not included in the LRFD
database. Because the databases are different for each code, comparisons are not made
between codes, but are only made between the codes and the proposed model.
Table 5- Comparison of the proposed model with the design codes
LRFD Database
(155 tests)
EC Database
(311 tests)
CSA Database
(309 tests)
Statistical
parameter
Proposed
model
LRFD
*
LRFD
**
Proposed
model
EC
*
EC
**
Proposed
model
CSA
*
CSA
**
Average
strength ratio
1.09 1.56 1.95 1.08 1.93 1.93 1.09 2.69 3.73
Standard
deviation
0.31 0.64 0.8 0.29 0.71 0.71 0.29 1.57 2.18
COV 0.28 0.41 0.41 0.27 0.37 0.37 0.27 0.58 0.58
Unconservative
results, %
44.5 9.0 2.0 43.2 5.1 5.1 42.7 6.8 2.6
*Do not include strength reduction factors
**Strength reduction factors included
It is desirable to have a model that accurately represents physical capacity
(average strength ratio) and that has limited variability (coefficient of variation, COV).
Based on these metrics, the proposed IST model is superior to the current code models.
The average strength ratio of the proposed model is 1.08 to 1.09. This is a 30% to 60%
improvement over the accuracy of the code models when strength reduction factors are
not included. When strength reduction factors are included, the improvement is 44% to
60
70%. Scatter is also reduced in the proposed model. COV, a metric indicating the
consistency level of the accuracy ranges from 0.27 to 0.28 for the proposed model, which
represents a 32% to 53% improvement over the code models.
In addition to being accurate in an average sense, it is also desirable for the
accuracy to be consistent across different values of input parameters. Fig. 8 compares
accuracy of the proposed and code models as a function of compressive strength of
concrete. Lines shown in the figure are the moving average using 20 data points. The
moving average line for the proposed model is consistently closer to a strength ratio of
1.0. While the proposed model is superior in terms of accuracy across the range of
variables, it is not as conservative as the LRFD, EC, and CSA models. The next section
discusses how safety can be considered when using the proposed model.
Fig. 8- Comparison of the performance of the proposed model (PM) and LRFD, EC, and
CSA through moving average of datasets
EC LRFD
61
Conservatism of the Proposed Model
At the outset of this section, it is acknowledged that modern codes are based on
relatability theory and that reliability is the preferable means for addressing safety of the
proposed IST model. Such analyses are recommended for future work, but are beyond the
scope of the current paper. A Strength Adjustment Factor (SAF) as an alternative -albeit
less rigorous- method is presented to address conservatism of the proposed model.
Fig. 9 presents the percent of unconservative results that occur for different
levels of SAF. As the SAF increases, the number of unconservative results decreases and
the model become safer. For the NWC dataset, the percent of unconservative results was
5%, 1.2% and 0.4% for SAF equal to 1.5, 1.75 and 2.0, respectively. The LWC dataset
had 6% and 0% unconservative results, when SAF is equal to 1.5 and 1.75, respectively.
The lowest percent of unconservative results from the code models was 2.0% (Table 5).
Thus SAF of 1.75 produces a similar degree of conservatism as the codes, and SAF of 2.0
produces a greater degree of conservatism than the codes. In the absence of a reliability
analysis, a SAF of 1.75 is recommended when applying the proposed model.
62
Fig. 9- Percentage of unconservative results for different SAF
Summary and Conclusions
Artificial Neural Networks (ANN) and multiple linear regression analyses were
used to study Interface Shear Transfer (IST) and to develop a new IST design model.
Sensitivity analyses were conducted using ANN models; creation of the proposed design
model was based on the linear regression analysis. Modeling and analyses considered
members with normal weight concrete (NWC) and light weight concrete (LWC). Source
data for the modes came from a database presented in a previous paper (Soltani and Ross
2016). Design variables in the analyses included compressive strength of concrete ( ),
area of concrete interface ( ), interface shear reinforcement index ( , applied
normal stress ( ), and roughness amplitude of interface ( ). The proposed model was
compared to the IST models from three design codes: AASHTO LRFD 2014, Eurocode 2
2004, and CSA A23.3-14 2014. Finally, a Factor of Safety (FS) approach was presented
63
for addressing conservatism of the proposed model. Salient conclusions and observations
are as follows:
The ANN and multiple linear regression models were able to represent the
experimental IST capacities with a high level of confidence. The lowest R2 value
for any model in the study was 0.89. The R2 value of the ANN models were
approximately 4% higher than for the multiple linear regression models.
Sensitivity analyses demonstrated each of the considered design variables are
approximately linearly influential on IST strength. Among the variables,
compressive strength of concrete was the most influential. Notably, this parameter
is only indirectly considered in IST capacity of LRFD, EC, and CSA design
codes; compressive strength of concrete is only considered in upper-bound
equations for IST strength.
The proposed design model is accurate when compared to the experiential data.
The average strength ratio of the model was 1.06. The COV of the model was
0.26, a 32% to 53% improvement over current codes. Most significantly, the
proposed model produces consistent levels of accuracy for different values of the
design variables.
A strength adjustment factor value of 1.75 applied to the proposed model
produces unconservative results in 1.2% to 0% of experimental cases for normal-
weight and light-weight concrete, respectively. These percentages are more
conservative than to the 2% to 5% of unconservative cases resulting from current
code models.
64
Notation
The following symbols are used in this paper:
= Area of concrete considered to be engaged in interface shear transfer
= Area of interface shear reinforcement crossing the shear plane within the area
= Permanent net compressive force normal to the shear plane
= Roughness amplitude of interface
= IST strength of test using Artificial Neural Network
= Nominal IST strength of the concrete member
= Experimental IST strength
= Nominal IST strength
= Predicted IST strength from multiple regression analysis
= Cohesion factor
= Yield stress of reinforcement
= Compressive strength of concrete
n = Sample size
= Number of model parameters
= Friction factor
= Interface shear reinforcement index
= Applied normal stress
65
References
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Transfer in Reinforced Concrete Members.” ACI Structural Journal, in press.
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[8] Birkeland, P. W., & Birkeland, H. W. (1966). “Connections in precast concrete
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(2006). “Predicting the compressive strength and slump of high strength concrete
using neural network.” Construction and Building Materials, 20(9), 769-775.
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[19] Cladera, A., & Mari, A. R. (2004). “Shear design procedure for reinforced
normal and high-strength concrete beams using artificial neural networks. Part I:
beams without stirrups.” Engineering Structures, 26(7), 917-926.
[20] Sanad, A., and Saka, M. P. (2001). “Prediction of ultimate shear strength
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[23] Bai, J., Wild, S., Ware, J. A., & Sabir, B. B. (2003). “Using neural
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69
CHAPTER FOUR
EVALUATION OF A 4-POINT BENDING TEST METHOD FOR INTERFACE
SHEAR TRANSFER IN CONCRETE MEMBERSi
Introduction
Interface Shear Transfer theory (hereafter referred to as “IST”) is a model for the
mechanisms by which shear forces are transferred across an interface between two
concrete members. One important application of this concept is in the connection
between a precast bridge girders and cast-in-place concrete decks as illustrated in Fig. 1.
Composite action between the girder and deck, and therefore bridge stiffness and
strength, relies on the capacity of the interface to transfer shear forces. The IST theory
will be discussed in more detail in the section “BACKGROUND”.
The push-off method (hereafter referred to as “PO”) (Fig. 2) is conventionally
used to test IST in Reinforced Concrete (RC) members. This test method was first used
by Hofbeck et al. in 1969 [1]. In this test method, two L-shaped concrete elements are
cast having a common interface. A force is applied from one end of the test specimen,
while the other end is supported as shown in Fig. 2. The test can be conducted vertically
or horizontally. Load is applied concentrically with the interface, thus direct shear (no
moment) acts on the interface.
i Soltani, M., & Ross, B. E., “Evaluation of A 4-Point Bending Test Method for Interface Shear Transfer in
Concrete Members,” submitted (under review), 2016.
70
Fig. 1-Interface shear transfer between precast girder and cast-in-place deck
Fig. 2- Conventional IST test method, push-off
The Iosipescu V-notched 4-point bending shear test method (hereafter referred to
as “VN”) (Fig. 3) was originally proposed by Iosipescu in 1967 [2] for measuring the
71
shear strength of isotropic and homogenous materials, such as metals. The Iosipescu
shear test uses a uniform thickness test specimen which has two 90-degree V-shaped
notches on either sides of the shear interface. A large force is applied on the edge of the
notch, P, and a relatively small load, P’, is applied at the end of the test specimen. Shear
passes through the notched section with no moment as shown in Fig. 3.
Fig. 3- V-Notched Iosipescu 4-point bending test method
The objective of this paper is to introduce and evaluate the VN test method as an
alternative for testing IST in reinforced concrete members. Pros and cons of these the VN
and PO methods are compared and contrasted in this study. An experimental program and
finite element analysis are used as comparative tools. Ease of fabrication of test
specimens and test protocols are also compared and contrasted.
Background
Interface Shear Transfer
Shear diagram
Moment diagram
72
In IST, shear forces are carried through three mechanisms: cohesion between
concrete surfaces across the interface, shear-friction, and dowel action from
reinforcement that crosses the interface [3],[4]. The cohesion is the concrete bond due to
the adhesion between concrete interface surfaces. Some researchers have also included
aggregate interlock as a sub-mechanism of cohesion [4]. The shear-friction concept was
proposed by Mast [5] and Birkeland and Birdeland [6] to explain shear force transfer
across cracks in RC members. The shear-friction mechanism is explained in the
subsequent paragraph. Dowel action is caused by direct shear force passing through the
interface reinforcement. At low load levels, the shear force is resisted almost exclusively
through cohesion. At higher load, however, cracks are formed and cohesion is broken,
resulting in forces being carried by a combination of shear-friction and dowel action.
The shear-friction concept is explained based on a saw-tooth model as shown in
Fig. 4. As the elements on either side of the interface slide relative to each other, the
roughness of the interface causes separation in a direction perpendicular to the interface.
This perpendicular separation to the interface creates tension in the interface
reinforcement. Tension in the reinforcement creates a normal force at the interface. The
normal force then creates friction at the interface that resists horizontal displacement.
This mechanism is the basis for shear-friction provisions of the ACI 318-14 design code
[7].
73
Fig. 4-Saw-tooth model (after Santos and Julio [4])
Hsu et al. [8] investigated transfer of shear across initially uncracked planes,
where concrete bond at the interface must be broken prior to engaging the shear-friction
and dowel action mechanisms. The cohesion and shear-friction mechanisms are the basis
for IST provisions of AASHTO LRFD 2014 [9], Eurocode 2 [10], and CSA A23.14 [11]
design codes.
Interface Shear Transfer Test Methods
There have been many different test methods used to test IST (Fig. 5). The slant-
shear and splitting tests (Fig. 5 (a) and (d)) were used by Santos and Julio [12]; the pull-
off test (Fig. 5 (c)) was used originally by Mattock and Hawkins [13]; the corbel with
moment test (Fig. 5 (b)) was applied by Johal [14]; and the beam test (Fig. 5 (e)) was
conducted originally by Loov and Patnaik [15]. However, most IST studies have utilized
the PO (Fig. 2) method [1],[16],[17]. The current study therefore, is focused on the PO as
the most common IST test method. The PO can be conducted horizontally, as shown in
Fig. 6 [18]. In this set-up, normal forces perpendicular to the interface can be applied by
simply adding dead load to the top of the specimen.
74
(a) Splitting (b) Corbel with moment (c) Pull-off
(d) Slant-shear (e) Beam
Fig. 5- Interface shear transfer test methods
Fig. 6- Horizontal set-up of the push-off test
75
Iosipescu 4-Point Bending Test and Its Application to RC Members
Since its inception, the Iosipescu test has been used to characterize the shear
strength of many different materials. For example, ASTM Standard D5379 [19] is a
modified version of the Iosipescu 4-point bending method, which is used for testing shear
properties of fiber-polymer laminated composites. Modified versions of the test have also
been applied to concrete. Ross [20] tested shear strength of concrete reinforced by
external Fiber-Reinforced Polymer (FRP) material using a modified Iosipescu shear test.
The program included analytical and experimental work. In order to increase shear
capacity of concrete members, external FRP reinforcement was scrutinized. Unlike the
research conducted by Ross [20], the current study does not consider external FRP.
Guenther [21] and Guenther et al. [22] conducted experimental and analytical
programs to validate a modified Iosipescu 4-point bending test as a means of measuring
the direct shear of plain concrete sections. Finite element models were used to study the
effects of different load configurations on the distribution of shear stress at the interface.
Experiments were also conducted. Test specimens did not contain interface
reinforcement, nor did the specimens include notches as proposed by Iosipescu. The
current study builds on the work of Guenther et al. and Ross by extending application of
the Iosipescu method to test IST in reinforced concrete members.
Analytical Program
Finite Element Analysis (FEA) of PO and VN tests were modeled using
ABAQUS CAE [23]. The models were linear elastic with 2D Shell Planar (plane-stress)
elements having 2.54cm (1in.) thickness. The models did not include reinforcement and
76
assumed monolithic concrete. Fig. 7 shows the meshed model, load, and support
configurations. Load magnitudes, load locations, and support locations were designed to
create an interface shear of 22.2 kN (5 kip) for both models. The length of the interface
was 20.3 cm (8in.). Shear and normal stress distributions of the models along the length
of interface were considered. A mesh convergence study was conducted as a part of the
analysis as is discussed in a subsequent paragraph.
Fig. 7- Meshing, boundary condition, and loading configuration of analytical program,
VN model (left) and PO model (right)
Stress distributions along the interface are presented in Fig. 8. For both types of
specimens, the maximum shear stress occurred at the edges of the interface, while the
minimum shear stress occurred at the midpoint of the interface. The maximum tensile
normal stress occurred at the interface edges, while the maximum compression stress
77
occurred at the midpoint of the interface. In the normal stress graph (Fig. 8 right), the
tensile and compressive stresses are shown with negative and positive values,
respectively.
Fig. 8- Shear stress (left) and normal stress (right) for PO vs. VN
To quantitatively compare the PO and VN stress states at the interface, stress at a
point 1.25cm (0.5in.) from the end was selected (Fig 8). This point was chosen because it
is near the locations of extreme stresses, but has stress values that coverage when mesh
density is increased. Stresses at the ends of the interface of the PO model do not
converge with increased mesh density. Results of a mesh convergence study for the
selected point are presented in Fig. 9. The results indicate that an element size of 0.25cm
(0.1in.) produces stability of stress distribution for both models. Thus, quantitative
comparisons between the models are made at a point 1.25cm (0.5in.) from the end and
with a model having a nominal element size of 0.25cm (0.1in.).
C T
78
Fig. 9- Mesh convergence study of Shear stress (left) and normal stress (right) for PO vs.
VN (the squares show the point used to conduct the convergence study)
The VN model had much lower concentration of shear stress (50% lower) at the
comparison point relative to the PO model (Fig. 8). Additionally, the normal stress
(perpendicular axis of shear interface) at the comparison point in VN test was -2.41 MPa
(-0.35 ksi); this is a lower stress compared to the -2.90 MPa (-0.42 ksi) stress in the PO
model. At the comparison point normal stress of VN model was 17% lower than PO
model.
Abrupt change of the cross-section in the PO model caused a stress concentration
at the edge of the interface. In contrast to the PO model, the VN model results in a
relatively uniform distribution of the shear stress across the interface. Therefore, the
elastic (prior to cracking) stress distribution of the VN model is much closer to the stress
distribution of the cast-in-place deck and bridge girder connection (Fig. 1).
Point of comparison
79
While the analytical program did not include the interface roughness,
reinforcement, and nonlinear properties, nevertheless, it demonstrated the effects of the
test methods on the elastic stress state of the interface. The geometry and loading of the
PO tests leads to stress concentrations at the interface edges. By comparison, the
magnitudes of the extreme stresses in the VN tests are lower.
Experimental Program
Specimen Details and Materials
An experimental program was also conducted to compare and contrast the PO and
VN test methods. The experimental test matrix is shown in Table 1 and based on the
nomenclature in Fig. 10. The test program was conducted with eight VN members and
eight PO members. All specimens had interface area of 206.4 cm2 (32 in2), 10.1cm (4in.)
width and 20.2cm (8in.) length. Variables in the test program included interface
roughness condition and type of test. Two different interface conditions were included:
intentionally roughened to amplitude of 6mm (0.25in.) (R) and smooth with no
roughened amplitude (S).
Table 1- Test matrix of experimental program
Specimen
type
Replicates Specimen ID Test
Type
Reinforcement Interface
Condition # and
size
Avf, cm2
(in2)
NR 4 NR1, NR2,
NR3, NR4
VN 4#3 2.84
(0.44)
R
NS 4 NS1, NS2,
NS3, NS4
VN 4#3 2.84
(0.44)
S
PR 4 PR1, PR2,
PR3, PR4
PO 4#3 2.84
(0.44)
R
PS 4 PS1, PS2,
PS3, PS4
PO 4#3 2.84
(0.44)
S
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Fig. 10- Nomenclature of test specimens
All the reinforcement used in program were metric bar size of #10 (imperial bar
size of #3). Concrete and reinforcement material properties are listed in Table 2. All
specimens were cast with the same concrete batch and at the same time during the fall of
2015. The aggregate was crushed stone having a maximum size of 17mm (0.75in.);
water-to-cement ratio of 0.54; and the slump was 102mm (4in.).
Test Procedure
PO and VN test specimens were tested using the set-ups shown in Fig. 11. PO
specimens were placed horizontally and pushed from the top of the specimens. A steel I-
beam was used as spreader at top of the VN specimens to apply load. Knowing the load
and geometry of the spreader, the reactions on the spreader (loads on the specimen) could
be determined through Statics. In this manner, the set-up for the VN specimens was also
statically determinate.
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Table 2-Material properties
Material Properties
Concrete 28-day compressive strength of layer 1 18.1 MPa (2.62 ksi)
28-day compressive strength of layer 2 17.9 MPa (2.60 ksi)
38-day compressive strength of layer 1 19.1 MPa (2.77 ksi)
31-day compressive strength of layer 2 18.7 MPa (2.72 ksi)
55-day compressive strength of layer 1 20.0 MPa (2.90 ksi)
48-day compressive strength of layer 2 19.6 MPa (2.88 ksi)
Note: The same concrete was used for all specimens; all
were tested between 38 and 55 days after casting layer 1;
and/or 31 and 48 days after casting layer 2.
#3
Reinforcement
bars
ASTM A615-12 Gr 420/60
Yield strength 495.7 MPa (71,900 psi)
Tensile strength 764.6 MPa (110,900 psi)
Fig. 11- Loading configuration of experimental program, VN test (left) and PO test
(right)
Displacement and force was monitored and logged using a computer data
acquisition system. Two string potentiometers monitored the horizontal displacement
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(parallel to the interface), where each was attached to one layer of the specimens as
shown in Fig. 12. The load was applied using a hydraulic jack at a rate of approximately
0.22 kN per second (50 pounds per second) and was distributed from actuator to the
specimen through steel spreader plates and neoprene bearing pads. The applied load was
recorded using a pressure gage installed in the hydraulic line supplying the jack. Area of
the jack was 46.6 cm2 (7.2 in2), therefore the force was computed by multiplying the gage
pressure by the area of the jack. The pressure gage was calibrated just before conducting
the tests. The maximum IST capacity was determined from the peak load resisted by the
specimen.
Fig. 12- Installment configuration of string pods, VN test (left) and PO test (right)
Constructability Comparison of Test Methods
The reinforcement plans of two tests are shown in Fig. 13. The PO tests needed a
relatively more complicated reinforcement scheme to induce failure at the interface. The
VN tests had an easy-to-implement reinforcement plan, which required only straight bars.
83
Despite the reinforcement provided in the PO specimens, the first two PO specimens
tested in this study failed away from the interface. Thus, external steel plates were added
to the remaining PO specimen as shown in Fig. 14. Each of the specimens with the steel
plates failed as intended at the interface. Previous researchers have demonstrated that it is
possible to conduct successful PO tests without external steel plates if sufficient internal
reinforcement is provided [1],[16]. Regardless of the location (internal/external) of the
reinforcement, PO specimens require more complicated reinforcing schemes than do VN
specimens.
Fig. 13- Reinforcement plan of experimental program, VN (left) and PO (right)
In comparing test set-up configurations of the two test methods (Fig. 11), it is also
important to mention that external normal forces can be more easily applied to PO tests.
Such forces mimic dead loads in structures which can increase IST capacity. When
conducting horizontal PO tests (Fig. 6), a normal force perpendicular to the interface can
be introduced by simply placing a dead load on top of the specimen. Application of
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normal force to the interface of VN specimens would be more challenging. One
possibility would be the use of clamps which apply compressive forces at the ends of the
specimens. This condition was not addresses in the current test program.
Fig. 14- Stiffeners attached to the PO specimens
Experimental Results and Discussion
Experimental IST capacity (Vtest) was determined from the peak force recorded
during testing. For the PO test, experimental IST capacity is equal to the peak applied
force. For the VN test, experimental IST capacity was calculated from the peak applied
load, specimen geometry, and static equilibrium. The experimental program was
designed to elucidate basic similarities and differences between the two test methods
under roughened and smooth interface conditions. A comprehensive program, including
85
variation in specimen size, reinforcement quantity and concrete strength is recommended
as an extension of the current study.
Results of the test program are summarized in Fig. 15, where minimum,
maximum, and average capacities of each specimen type are presented. Shear-
displacement behaviors of the specimens are presented in Fig 16. Shear in the figure is
the applied interface shear force and displacement is movement of the sides parallel to the
interface.
Fig. 15- Results of the experimental program
Referring to Fig. 16 (left), the interface shear force corresponding to first slip
displacement was lower in PO tests as compared to VN tests, when the interfaces are
smooth. This result is attributed to the elastic stress conditions that occur in the
specimens prior to cracking. According to the FEA model, the PO test has higher stress
concentration compared to the VN. Consequently, the PO test specimens cracked and
experienced interface slip at loads lower than the VN specimens, which did not have the
same level of stress. A slip of 0.5mm (0.02in.) was selected to quantitatively compare
86
the shear force are first slip. The average interface shear force of the PO tests at this level
of slip was 38% lower than the VN tests at the same level.
Fig. 16- Interface shear versus interface horizontal slip graphs
For specimens with a smooth interface, the average IST capacity of the PO tests
was only 56% of the VN capacity. The additional capacity of the VN tests was the result
of binding action at the interface (Fig. 17). Slip displacement in the VN tests was
accompanied by rotation of the specimen halves. The applied loads near the interface, P,
were always applied vertically. As the specimen halves rotated, projected components of
P were a force parallel to the interface, , and a force perpendicular to the interface, .
The forces from the top and bottom supports created compression on the interface and
the binding mechanism. Forces generated an increase in the shear-friction resistance at
the interface, which ultimately led to an increase in the IST capacity of VN specimens.
Such binding action was not present in the PO specimens.
Roughened Interface
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The behavior of the specimens with roughened interfaces was distinct from the
behavior of specimens with smooth interfaces. Referring to Fig 16 (right), specimens
with roughened interfaces had similar shear forces at first crack for both test methods.
The average shear force at a slip of 0.5mm (0.02in.) was only 12% lower for the PO
specimens than for the VN specimens. Recall that the difference was 38% for the smooth
interface specimens. The reduced difference in the roughened-interface specimens is
attributed to stress concentrations occurring due to roughness of the interface; stress
concentrations due to roughness occur in both PO and VN specimens and partially
mitigate the effects of stress differences occurring due to test type. The FEA analysis did
not consider the effects of surface roughness and is not applicable to the roughened
interface specimens.
Fig. 17- Binding in the smooth interface of VN tests and application of normal force
The average IST capacity of the VN and PO test were only 5% different in the
specimens with roughened interfaces. This is different than was observed for smooth-
interface specimens, wherein binding action led to significantly higher IST capacity in
the VN tests. The roughened interface increased the stiffness of both the PO and VN
specimens when compared to the smooth-interface specimens. For the VN tests with
88
roughened interfaces, increased stiffness resulted in less slip displacement and rotation at
peak load. Because there was less slip and rotation, binding was not a factor in VN
specimens with rough interfaces. Thus, for roughened specimens the shear resistance at
the interface was similar for VN and PO, and the peak loads were similar.
Summary and Conclusion
The Iosipescu V-Notched 4-point bending test method (VN) was proposed to test
Interface Shear Transfer (IST) in reinforced concrete members. The VN method was
compared to the more conventional push-off (PO) test. Sixteen specimens were tested
with variables including the type of test (VN or PO) and the condition of the interface
(smooth or roughened). Ease of fabrication of test specimens and test protocols were also
compared and contrasted during the experimental program. Using finite element analysis,
an analytical program was also conducted to compare elastic (prior to cracking) stresses
in the VN and PO test specimens. Salient conclusions of this study are as follows:
The analytical program demonstrated that the VN model more closely simulates
the stress condition at the interface of cast-in-place decks and bridge girders. The
PO model resulted in stress concentrations at the interface ends that are not
present in the VN model.
Fabrication of the PO specimens was relatively more difficult than the VN
specimens. The reinforcement assembly of the PO specimens was more
complicated. In the PO specimens, additional external steel reinforcement was
required to prevent failure away from the interface.
89
The experimental program showed that the VN and PO had the similar IST
capacity (5% difference), when the interfaces were roughened. Additional tests
are recommended to confirm that this result is generally applicable under a
broader range of conditions.
The experimental program demonstrated that the VN and PO are not comparable
for smooth interface specimens. For such smooth interfaces, the average IST
strength of VN specimens was 79% greater than that of the PO specimens. The
increased capacity of the VN specimens is attributed to binding action that occurs
at the interface when the slip displacement and rotation are large.
Although the effects of external normal forces applied to the interfaces was not
considered in the test program, it is noted that application of normal force is relatively
more difficult in VN tests compared to the PO tests. This benefit of the PO tests is
also worth considering when selecting a test method.
References
[1] Hofbeck, J. A., Ibrahim, I. O., & Mattock, A. H. (1969, February). Shear transfer in
reinforced concrete. In Journal Proceedings (Vol. 66, No. 2, pp. 119-128).
[2] Iosipescu, N. (1967). New accurate procedure for single shear testing of metals. J
MATER, 2(3), 537-566.
[3] Jimenez-Perez, R., Gergely, P., & White, R. N. (1978). Shear transfer across cracks
in reinforced concrete (No. PB-288885). Cornell Univ., Ithaca, NY (USA).
[4] Santos, P. M., & Júlio, E. N. (2012). A state-of-the-art review on shear-
friction. Engineering Structures, 45, 435-448.
90
[5] Mast, R. F. (1968). Auxiliary reinforcement in concrete connections. Journal of the
Structural Division.
[6] Birkeland, P. W., & Birkeland, H. W. (1966, March). Connections in precast concrete
construction. In ACI journal, Proceedings (Vol. 63, No. 3, pp. 345-367).
[7] ACI Committee, American Concrete Institute, & International Organization for
Standardization. (2014). Building code requirements for structural concrete (ACI
318-14) and commentary. American Concrete Institute.
[8] Hsu, T. T., Mau, S. T., & Chen, B. (1987). Theory on shear transfer strength of
reinforced concrete. Structural Journal, 84(2), 149-160.
[9] American Association of State Highway and Transportation Officials (AASHTO).
(2014). AASHTO LRFD bridge design specifications. 7th edition, Washington, D.C:
[10] British Standards Institution. (2004). Eurocode 2: Design of Concrete Structures.
London. UK.
[11] Canadian Standard Association (CSA). (2014). CSA Standard A23.3-14,
Canadian Standard Association, Ontario, Canada.
[12] Santos, P. M. D., & Júlio, E. N. B. S. (2011). Factors affecting bond between new
and old concrete. ACI Materials Journal, 108(4), 449-456.
[13] Mattock, A. H., & Hawkins, N. M. (1972). Shear transfer in reinforced concrete-
recent research. PRECAST/PRESTRESSED CONCRETE INSTITUTE.
JOURNAL, 17(2).
[14] Johal, L. (1975). Shear transfer in reinforced concrete with moment or tension
acting across the shear plane. PCI JOURNAL, 77.
91
[15] Loov, R. E., & Patnaik, A. K. (1994). Horizontal shear strength of composite
concrete beams with a rough interface. PCI Journal, 39(1), 48-69.
[16] Mattock, A. H., Li, W. K., & Wang, T. C. (1976). Shear transfer in lightweight
reinforced concrete. PCI journal, 21(1), 20-39.
[17] Walraven, J., Frenay, J., & Pruijssers, A. (1987). Influence of concrete strength
and load history on the shear friction capacity of concrete members. PCI
journal, 32(1), 66-84.
[18] Banta, T. E. (2005). Horizontal shear transfer between ultra high performance
concrete and lightweight concrete (Doctoral dissertation, Virginia Polytechnic
Institute and State University).
[19] Standard, A. S. T. M. (1997). Standard test methods for shear properties of
composite materials by the v-notched beam method. West Conshohocken (PA):
ASTM, 100.
[20] Ross, B. E. (2002). Analytical modeling and standardized testing of concrete
beams with web bonded FRP shear reinforcement. In Masters Abstracts
International (Vol. 45, No. 06).
[21] Guenther, C. L. (2007). Evaluation of shear and diagonal tension in plain
concrete. ProQuest.
[22] Helmick, C. G., Toker-Beeson, S., & Tanner, J. E. Evaluation of Shear and
Diagonal Tension in Plain Concrete.
[23] Abaqus manual guide (2014). Version 6.14-1. Dassault Systémes Simulia Corp.,
Providence, RI.
92
CHAPTER FIVE
SUMMARY AND CONTRIBUTIONS
This dissertation is motivated by the desire to understand interface shear transfer
and to provide engineers with better tools for designing reinforced concrete structures
that resist interface shears. Toward that end, this research leveraged database studies,
neural networks and statistical models, and physical experimentation.
Much of the work in this dissertation is based on a newly-compiled
comprehensive database of uncracked RC members tested in Interface Shear Transfer
(hereafter referred to as “IST”). The database was used to evaluate the IST provisions of
different design codes and to identify limitations of the current codes. Subsequent work
was motivated by the desire to create a new design model, which corrects the limitations
of the current design codes. In the final portion of the dissertation research, a new 4-point
bending IST test method was introduced, demonstrated, and compared to the most
conventional IST test method, the push-off test. The new test method can reduce the
effort required to experimentally assess IST capacity. The key findings, contributions,
and significance of this dissertation are presented in Table 1.
93
Table 1- Key findings and significance of different phases in this study
Phase/
Chapter
Key Findings/ Contributions Significance
Phase 1/
Chapter 2
Creation of a comprehensive
database of uncracked IST
members
Largest database of uncracked IST
members complied to date.
Evaluation of the IST models of
LRFD, EC, and CSA
Code-based models showed inaccuracy
and inconsistency throughout the range
of design variables.
Phase 2/
Chapter 3
Compressive strength of concrete
was the most influential design
parameter affecting the IST
strength
Compressive strength of concrete is
indirectly considered in code-based
models. This is one limitation of the
current codes.
A new IST design model was
proposed
The proposed model improved the
limitations of code-based models; it
directly considered compressive strength
of concrete and is more accurate and
consistent throughout the range of
design variables.
Phase 3/
Chapter 4
Demonstration of the Iosipescu
V-Notched 4-point bending (VN)
test method for testing IST
VN tests can decrease the effort required
for testing IST; compared to Push-Off
(PO) tests, VN test specimens were
relatively easier to fabricate.
VN tests mimic the interface stress
distribution at cast-in-place deck to
bridge girders connections.
For specimens with roughened
interfaces, VN test results were similar
to PO tests results.
In the first phase of this dissertation, a comprehensive database of uncracked IST
members was created, which contained 774 tests from research conducted from 1969 to
2015. To date, this is the largest database that has been complied for uncracked IST
specimens. Code-based IST models from three different major concrete design codes,
94
including LRFD, EC, and CSA, were evaluated using the database. When strength
reduction factors were not considered, the average experimental-to-nominal strength ratio
(strength ratio) of the LRFD, EC, and CSA were 1.49, 1.93, and 2.59, respectively. The
coefficient of variation of the aforementioned design codes were 0.38, 0.37, and 0.80,
respectively. The strength ratios were not consistent throughout the range of design
variables. Hence, IST provisions of these design codes showed inaccuracy and
inconsistency of accuracy throughout the range of design variables, and therefore is ripe
for improvement.
In the second phase of this dissertation, a sensitivity analysis was conducted to
determine the effects of compressive strength of concrete, reinforcement index, interface
cross-sectional area, roughness amplitude, and interface normal force on IST strength.
The analysis was conducted using artificial neural networks. It was shown that each
parameter was approximately linearly related to the IST strength of concrete members.
The compressive strength of concrete was the most influential among the design
variables; however, compressive strength of concrete is only indirectly considered in
code-based IST models. Based the results of the sensitivity analysis, a new design model
was proposed, which model was derived using multiple-linear regression analysis. The
proposed design model has a high level of correlation with the experimental data, with a
minimum R2 value of 0.88. The proposed design model alleviated limitations of the
current design codes by producing more accurate and more consistent results throughout
the range of design variables.
95
Finally, the Iosipescu V-Notched 4-point bending test method was demonstrated
for testing IST of reinforced concrete members. This test method was compared to the
most conventional IST test method, the push-off test. The 4-point bending tests reduced
the effort required for testing IST compared to the PO tests, largely because VN test
specimens were relatively easier to fabricate. Results of the demonstrations showed that
when specimen interfaces were roughened, the IST strength of new 4-point bending
specimens were similar to specimens tested using the traditional method.
96
APPENDICES
97
Appendix A
List OF REFERENCES FOR THE ACI DATABASE PAPER AND DATABASE
EVALUATION
All references collected to develop the database are listed in Appendix A along with
number of tests used in the final databases.
Reference Total
tests
Tests included
after initial
filtering
Tests included in final databases Reasons for exclusion
in initial filtering LRFD EC CSA
Shaw and Sneed
2014 [36]
36 36 36 36 36 -
Harries et al. 2012
[37]
8 8 0 8 8 -
Santos and Julio 2011
[38]
60 30 0 30 30 Splitting tests
Scott 2010 [39] 36 27 18 27 27 Failure of deck
Zeno 2009 [40] 8 8 8 8 8 -
Mansur et al. 2008
[41]
19 19 19 19 19 -
Banta 2005 [42] 24 20 10 20 20 Undefined
interface roughness
Kahn and Slapkus
2004 [27]
6 3 3 3 3 Flexural failure
Gohnert 2003 [43] 90 90 0 90 90 -
Kahn and Mitchell
2002 [13]
50 31 23 12 31 Pre-cracked tests
Papanicolaou and
Triantafillou 2002 [44]
36 36 0 0 0 -
Gohnert 2000 [16]
12 12 0 12 12 -
Valluvan et al. 1999
[44]
16 14 5 7 7 Grout at interface
Loov and Patnaik
1994 [25]
16 13 13 13 11 Flexural failure
Walraven and
Stroband 1994 [46]
6 0 0 0 0 Pre-cracked tests
Hoff 1993 [47] 18 0 0 0 0 Pre-cracked tests
Hsu et al. 1987 [14] 26 26 26 26 26 -
Frénay 1985 [48] 20 0 0 0 0 Pre-cracked tests
Pruijssers 1985 [49] 13 0 0 0 0 Pre-cracked tests
98
Walraven and
Reinhardt 1981 [50]
52 0 0 0 0 Pre-cracked tests
Mattock et al. 1976
[28]
60 27 24 0 27 Pre-cracked tests
Mattock 1976 [51] 31 0 0 0 0 Pre-cracked tests
Mattock et al. 1975
[52]
27 7 7 0 7 Corbel and pre-
cracked tests
Mattock and
Hawkins 1972 [10]
66 6 6 0 6 Pull-off and Pre-
cracked tests
Hofbeck et al. 1969
[9]
38 15 14 0 15 Pre-cracked tests
Total 774 428 220 311 383
The detailed information of the 383 tests included in the evaluation of final database is
shown as follows:
specimens
ID Acv,
cm2
(in2)
f'c,
Mpa
(ksi)`
Avf,
cm2
(in2)
Fy,
Mpa
(ksi)
Pc,
kN
(kip)
Vexp,
kN
(kip)
Weight
**
Ro
ugh
.
**
*
Code-specific
databases
LRFD EC CSA
Shaw and Sneed 2014 [32]
N-5-R-4 319.3
(49.5)
33.8
(4.9)
4.5
(0.7)
456.4
(66.2) 0.0
263.0
(59.1)
NWC R2 X X X
N-5-R-5 319.3
(49.5)
33.8
(4.9)
4.5
(0.7)
456.4
(66.2) 0.0
237.6
(53.4)
NWC R2 X X X
N-5-R-6 319.3
(49.5)
33.8
(4.9)
4.5
(0.7)
456.4
(66.2) 0.0
237.6
(53.4)
NWC R2 X X X
N-5-S-4 319.3
(49.5)
33.8
(4.9)
4.5
(0.7)
456.4
(66.2) 0.0
145.5
(32.7)
NWC S X X X
N-5-S-5 319.3
(49.5)
33.8
(4.9)
4.5
(0.7)
456.4
(66.2) 0.0
154.4
(34.7)
NWC S X X X
N-5-S-6 319.3
(49.5)
33.8
(4.9)
4.5
(0.7)
456.4
(66.2) 0.0
174.0
(39.1)
NWC S X X X
S-5-R-1 319.3
(49.5)
31.0
(4.5)
4.5
(0.7)
456.4
(66.2) 0.0
227.8
(51.4)
LWC R2 X X X
S-5-R-2 319.3
(49.5)
31.0
(4.5)
4.5
(0.7)
456.4
(66.2) 0.0
224.3
(50.4)
LWC R2 X X X
S-5-R-3 319.3
(49.5)
31.0
(4.5)
4.5
(0.7)
456.4
(66.2) 0.0
239.8
(53.9)
LWC R2 X X X
S-5-S-1 319.3
(49.5)
31.0
(4.5)
4.5
(0.7)
456.4
(66.2) 0.0
171.3
(38.5)
LWC S X X X
S-5-S-2 319.3
(49.5)
31.0
(4.5)
4.5
(0.7)
456.4
(66.2) 0.0
151.7
(34.1)
LWC S X X X
S-5-S-3 319.3
(49.5)
31.0
(4.5)
4.5
(0.7)
456.4
(66.2) 0.0
177.1
(39.8)
LWC S X X X
A-5-R-1 319.3 42.1 4.5 456.4 0.0 215.4 LWC R2 X X X
99
(49.5) (6.1) (0.7) (66.2) (48.4)
A-5-R-2 319.3
(49.5)
42.1
(6.1)
4.5
(0.7)
456.4
(66.2) 0.0
235.0
(52.8)
LWC R2 X X X
A-5-R-3 319.3
(49.5)
42.1
(6.1)
4.5
(0.7)
456.4
(66.2) 0.0
228.7
(51.4)
LWC R2 X X X
A-5-S-1 319.3
(49.5)
42.1
(6.1)
4.5
(0.7)
456.4
(66.2) 0.0
184.7
(41.5)
LWC S X X X
A-5-S-2 319.3
(49.5)
42.1
(6.1)
4.5
(0.7)
456.4
(66.2) 0.0
178.4
(40.1)
LWC S X X X
A-5-S-3 319.3
(49.5)
42.1
(6.1)
4.5
(0.7)
456.4
(66.2) 0.0
174.4
(39.2)
LWC S X X X
N-8-R-1 319.3
(49.5)
51.7
(7.5)
4.5
(0.7)
456.4
(66.2) 0.0
329.3
(74.0)
NWC R2 X X X
N-8-R-2 319.3
(49.5)
51.7
(7.5)
4.5
(0.7)
456.4
(66.2) 0.0
249.6
(56.1)
NWC R2 X X X
N-8-R-3 319.3
(49.5)
51.7
(7.5)
4.5
(0.7)
456.4
(66.2) 0.0
285.2
(64.1)
NWC R2 X X X
N-8-S-1 319.3
(49.5)
51.7
(7.5)
4.5
(0.7)
456.4
(66.2) 0.0
291.9
(65.6)
NWC S X X X
N-8-S-2 319.3
(49.5)
51.7
(7.5)
4.5
(0.7)
456.4
(66.2) 0.0
237.2
(53.3)
NWC S X X X
N-8-S-3 319.3
(49.5)
51.7
(7.5)
4.5
(0.7)
456.4
(66.2) 0.0
246.1
(55.3)
NWC S X X X
S-8-R-1 319.3
(49.5)
49.6
(7.2)
4.5
(0.7)
456.4
(66.2) 0.0
320.4
(72.0)
LWC R2 X X X
S-8-R-2 319.3
(49.5)
49.6
(7.2)
4.5
(0.7)
456.4
(66.2) 0.0
299.9
(67.4)
LWC R2 X X X
S-8-R-3 319.3
(49.5)
49.6
(7.2)
4.5
(0.7)
456.4
(66.2) 0.0
296.8
(66.7)
LWC R2 X X X
S-8-S-1 319.3
(49.5)
49.6
(7.2)
4.5
(0.7)
456.4
(66.2) 0.0
298.1
(67.0)
LWC S X X X
S-8-S-2 319.3
(49.5)
49.6
(7.2)
4.5
(0.7)
456.4
(66.2) 0.0
257.6
(57.9)
LWC S X X X
S-8-S-3 319.3
(49.5)
49.6
(7.2)
4.5
(0.7)
456.4
(66.2) 0.0
262.6
(58.9)
LWC S X X X
A-8-R-1 319.3
(49.5)
53.8
(7.8)
4.5
(0.7)
456.4
(66.2) 0.0
275.0
(61.8)
LWC R2 X X X
A-8-R-2 319.3
(49.5)
53.8
(7.8)
4.5
(0.7)
456.4
(66.2) 0.0
284.3
(63.9)
LWC R2 X X X
A-8-R-3 319.3
(49.5)
53.8
(7.8)
4.5
(0.7)
456.4
(66.2) 0.0
285.2
(64.1)
LWC R2 X X X
A-8-S-1 319.3
(49.5)
53.8
(7.8)
4.5
(0.7)
456.4
(66.2) 0.0
205.1
(46.1)
LWC S X X X
A-8-S-2 319.3
(49.5)
53.8
(7.8)
4.5
(0.7)
456.4
(66.2) 0.0
213.6
(48.0)
LWC S X X X
A-8-S-3 319.3
(49.5)
53.8
(7.8)
4.5
(0.7)
456.4
(66.2) 0.0
230.1
(51.7)
LWC S X X X
Harries et al. 2012 [33]
615-3 A 1034.6
(160.4)
40.0
(5.8)
4.5
(0.7)
464.0
(67.3) 0.0
500.4
(112.5)
NWC R2 X X X
615-3 B 1052.6 40.0 4.5 464.0 0.0 429.2 NWC R2 X X X
100
(163.2) (5.8) (0.7) (67.3) (96.5)
615-4 A 1064.2
(165.0)
40.0
(5.8)
7.7
(1.2)
424.0
(61.5) 0.0
509.3
(114.5)
NWC R2 X X X
615-4 B 1048.1
(162.5)
40.0
(5.8)
7.7
(1.2)
424.0
(61.5) 0.0
509.3
(114.5)
NWC R2 X X X
1035-3 A 1015.9
(157.5)
40.0
(5.8)
4.5
(0.7)
896.3
(130.0) 0.0
400.3
(90.0)
NWC R2 X X X
1035-3 B 1035.5
(160.7)
40.0
(5.8)
4.5
(0.7)
868.7
(126.0) 0.0
467.1
(105.0)
NWC R2 X X X
1035-4 A 1048.1
(162.5)
40.0
(5.8)
7.7
(1.2)
965.3
(140.0) 0.0
603.6
(135.7)
NWC R2 X X X
1035-4 B 1036.5
(160.7)
40.0
(5.8)
7.7
(1.2)
905.3
(131.3) 0.0
504.9
(113.5)
NWC R2 X X X
Santos and Julio 2011 [35]
LAC-L28-
slant
562.6
(87.2)
66.2
(9.6)*
0.0 - 272. 2
(61.2)
471.9
(106.1)
NWC S X X
WB-L28-
slant
562.6
(87.2)
66.2
(9.6)*
0.0 - 311.8
(70.1)
540.0
(121.4)
NWC R1 X X
SAB-L28-
slant
562.6
(87.2)
66.2
(9.6)*
0.0 - 481.7
(108.3)
834.9
(187.7)
NWC R1 X X
SHB-L28-
slant
562.6
(87.2)
66.2
(9.6) *
0.0 - 591.2
(132.9)
1024.4
(230.3)
NWC R1 X X
SH-L28-
slant
562.6
(87.2)
66.2
(9.6) *
0.0 - 661.0
(148.6)
1145.4
(257.5)
NWC R1 X X
LAC-L56-
slant
562.6
(87.2)
88.7
(11.7) *
0.0 - 270.4
(60.8)
468.8
(105.4)
NWC S X X
WB-L56-
slant
562.6
(87.2)
88.7
(11.7) *
0.0 - 404.8
(91.0)
701.5
(157.7)
NWC R1 X X
SAB-L56-
slant
562.6
(87.2)
88.7
(11.7) *
0.0 - 503.5
(113.2)
872.3
(196.1)
NWC R1 X X
SHB-L56-
slant
562.6
(87.2)
88.7
(11.7) *
0.0 - 646.8
(145.4)
1120.9
(252.0)
NWC R1 X X
SH-L56-
slant
562.6
(87.2)
88.7
(11.7) *
0.0 - 607.2
(136.5)
1052.4
(236.6)
NWC R1 X X
LAC-L84-
slant
562.6
(87.2)
72.4
(10.50)
*
0.0 -
251.8
(56.6)
436.4
(98.1)
NWC S X X
WB-L84-
slant
562.6
(87.2)
72.4
(10.50)
*
0.0 -
270.3
(60.1)
463.0
(104.1)
NWC R1 X X
SAB-L84-
slant
562.6
(87.2)
72.4
(10.50)
*
0.0 -
300.2
(67.5)
520.4
(117.0)
NWC R1 X X
SHB-L84-
slant
562.6
(87.2)
72.4
(10.50)
*
0.0 -
325.6
(73.2)
564.0
(126.8)
NWC R1 X X
SH-L84-
slant
562.6
(87.2)
72.4
(10.5) *
0.0 - 349.6
(78.6)
605.8
(136.2)
NWC R1 X X
LAC-E28-
slant
562.6
(87.2)
68.2
(9.9) *
0.0 - 227.3
(51.1)
394.1
(88.6)
NWC S X X
WB-E28- 562.6 68.2 0.0 - 261.5 453.3 NWC R1 X X
101
slant (87.2) (9.9) * (58.8) (101.9)
SAB-E28-
slant
562.6
(87.2)
68.2
(9.9) *
0.0 - 274.0
(61.6)
475.1
(106.8)
NWC R1 X X
SHB-E28-
slant
562.6
(87.2)
68.2
(9.9) *
0.0 - 311.8
(70.1)
540.0
(121.4)
NWC R1 X X
SH-E28-
slant
562.6
(87.2)
68.2
(9.9) *
0.0 - 324..3
(72.9)
561.8
(126.3)
NWC R1 X X
LAC-E56-
slant
562.6
(87.2)
71.0
(10.3) *
0.0 - 266.9
(60.0)
462.6
(104.0)
NWC S X X
WB-E56-
slant
562.6
(87.2)
71.0
(10.3) *
0.0 - 310.0
(69.7)
536.9
(120.7)
NWC R1 X X
SAB-E56-
slant
562.6
(87.2)
71.0
(10.3) *
0.0 - 354.5
(79.7)
614.7
(138.2)
NWC R1 X X
SHB-E56-
slant
562.6
(87.2)
71.0
(10.3) *
0.0 - 386.0
(86.6)
667.7
(150.1)
NWC R1 X X
SH-E56-
slant
562.6
(87.2)
71.0
(10.3) *
0.0 - 460.4
(103.5)
798.0
(179.4)
NWC R1 X X
LAC-E84-
slant
562.6
(87.2)
69.6
(10.1) *
0.0 - 180.1
(40.5)
312.3
(70.2)
NWC S X X
WB-E84-
slant
562.6
(87.2)
69.6
(10.1) *
0.0 - 185.5
(41.7)
321.6
(72.3)
NWC R1 X X
SAB-E84-
slant
562.6
(87.2)
69.6
(10.1) *
0.0 - 198.8
(44.7)
344.7
(77.5)
NWC R1 X X
SHB-E84-
slant
562.6
(87.2)
69.6
(10.1) *
0.0 - 221.5
(49.8)
383.9
(86.3)
NWC R1 X X
SH-E84-
slant
562.6
(87.2)
69.6
(10.1) *
0.0 - 270.9
(60.9)
469.3
(105.5)
NWC R1 X X
Scott 2010 [36]
LL-0-A 2477.4
(384.0)
40.3
(6.2)
0.0 - 11.1
(2.5)
587.2
(132.0)
LWC R2 X X
LL-0-B 2477.4
(384.0)
40.3
(6.2)
0.0 - 11.1
(2.5)
622.7
(140.0)
LWC R2 X X
LL-0-C 2477.4
(384.0)
40.3
(6.2)
0.0 - 11.1
(2.5)
791.8
(178.0)
LWC R2 X X
NN-0-A 2477.4
(384.0)
40.0
(6.1)
0.0 - 11.1
(2.5)
680.6
(153.0)
NWC R2 X X
NN-0-B 2477.4
(384.0)
40.0
(6.1)
0.0 - 11.1
(2.5)
711.7
(160.0)
NWC R2 X X
NN-0-C 2477.4
(384.0)
40.0
(6.1)
0.0 - 11.1
(2.5)
693.9
(156.0)
NWC R2 X X
NL-0-A 2477.4
(384.0)
40.3
(6.2)
0.0 - 11.1
(2.5)
827.4
(186.0)
LWC R2 X X
NL-0-B 2477.4
(384.0)
40.3
(6.2)
0.0 - 11.1
(2.5)
582.7
(131.0)
LWC R2 X X
NL-0-C 2477.4
(384.0)
40.3
(6.2)
0.0 - 11.1
(2.5)
876.3
(197.0)
LWC R2 X X
LL-1-A 2477.4
(384.0)
40.3
(6.2)
2.6
(0.4)
413.7
(60.0)
11.1
(2.5)
1076.5
(242.0)
LWC R2 X X X
LL-1-B 2477.4
(384.0)
40.3
(6.2)
2.6
(0.4)
413.7
(60.0)
11.1
(2.5)
653.9
(147.0)
LWC R2 X X X
LL-1-C 2477.4 40.3 2.6 413.7 11.1 836.3 LWC R2 X X X
102
(384.0) (6.2) (0.4) (60.0) (2.5) (188.0)
NN-1-A 2477.4
(384.0)
40.0
(6.1)
2.6
(0.4)
413.7
(60.0)
11.1
(2.5)
547.1
(123.0)
NWC R2 X X X
NN-1-B 2477.4
(384.0)
40.0
(6.1)
2.6
(0.4)
413.7
(60.0)
11.1
(2.5)
627.2
(141.0)
NWC R2 X X X
NN-1-C 2477.4
(384.0)
40.0
(6.1)
2.6
(0.4)
413.7
(60.0)
11.1
(2.5)
769.5
(173.0)
NWC R2 X X X
NL-1-A 2477.4
(384.0)
40.3
(6.2)
2.6
(0.4)
413.7
(60.0)
11.1
(2.5)
751.7
(169.0)
LWC R2 X X X
NL-1-B 2477.4
(384.0)
40.3
(6.2)
2.6
(0.4)
413.7
(60.0)
11.1
(2.5)
778.4
(175.0)
LWC R2 X X X
NL-1-C 2477.4
(384.0)
40.3
(6.2)
2.6
(0.4)
413.7
(60.0)
11.1
(2.5)
814.0
(183.0)
LWC R2 X X X
LL-3-A 2477.4
(384.0)
37.0
(5.7)
12.0
(1.9)
413.7
(60.0)
11.1
(2.5)
894.1
(201.0)
LWC R2 X X X
LL-3-B 2477.4
(384.0)
37.0
(5.7)
12.0
(1.9)
413.7
(60.0)
11.1
(2.5)
991.9
(223.0)
LWC R2 X X X
LL-3-C 2477.4
(384.0)
37.0
(5.7)
12.0
(1.9)
413.7
(60.0)
11.1
(2.5)
1023.1
(230.0)
LWC R2 X X X
NN-3-A 2477.4
(384.0)
40.0
(6.1)
12.0
(1.9)
413.7
(60.0)
11.1
(2.5)
867.4
(195.0)
NWC R2 X X X
NN-3-B 2477.4
(384.0)
40.0
(6.1)
12.0
(1.9)
413.7
(60.0)
11.1
(2.5)
969.7
(218.0)
NWC R2 X X X
NN-3-C 2477.4
(384.0)
40.0
(6.1)
12.0
(1.9)
413.7
(60.0)
11.1
(2.5)
1018.6
(229.0)
NWC R2 X X X
NL-3-A 2477.4
(384.0)
37.0
(5.7)
12.0
(1.9)
413.7
(60.0)
11.1
(2.5)
1076.5
(242.0)
LWC R2 X X X
NL-3-B 2477.4
(384.0)
37.0
(5.7)
12.0
(1.9)
413.7
(60.0)
11.1
(2.5)
1058.7
(238.0)
LWC R2 X X X
NL-3-C 2477.4
(384.0)
37.0
(5.7)
12.0
(1.9)
413.7
(60.0)
11.1
(2.5)
814.0
(183.0)
LWC R2 X X X
Zeno 2009 [37] P-615-3A 1034.8
(160.4)
40.0
(5.8)
4.3
(0.7)
464.0
(67.3) 0.0
500.4
(112.5)
NWC R2 X X X
P-615-3B 1052.9
(163.2)
40.0
(5.8)
4.3
(0.7)
464.0
(67.3)
0.0
429.2
(96.5)
NWC R2 X X X
P-615-4A 1064.5
(165.0)
40.0
(5.8)
7.6
(1.2)
424.0
(61.5) 0.0
509.3
(114.5)
NWC R2 X X X
P-615-4B 1048.4
(162.5)
40.0
(5.8)
7.6
(1.2)
424.0
(61.5) 0.0
573.8
(129.0)
NWC R2 X X X
P-1035-
3A
1016.1
(157.5)
40.0
(5.8)
4.3
(0.7)
896.3
(130.0) 0.0
400.3
(90.0)
NWC R2 X X X
P-1035-
3B
1036.8
(160.7)
40.0
(5.8)
4.3
(0.7)
868.7
(126.0) 0.0
467.1
(105.0)
NWC R2 X X X
P-1035-
4A
1048.4
(162.5)
40.0
(5.8)
7.6
(1.2)
965.3
(140.0) 0.0
603.6
(135.7)
NWC R2 X X X
P-1035-
4B
1036.8
(160.7)
40.0
(5.8)
7.6
(1.2)
897.0
(131.3) 0.0
504.9
(113.5)
NWC R2 X X X
Mansur et al. 2008 [38]
AN-2 359.3
(55.7)
40.0
(5.8) *
3.1
(0.5)
530.2
(76.9) 0.0
292.7
(65.8)
NWC S X X X
103
AN-4 359.3
(55.7)
40.0
(5.8) *
6.1
(1.0)
530.2
(76.9) 0.0
364.5
(81.9)
NWC S X X X
AN-6 359.3
(55.7)
40.0
(5.8) *
9.3
(1.4)
530.2
(76.9) 0.0
463.7
(104.2)
NWC S X X X
AM-2 359.3
(55.7)
68.9
(10.0) *
3.1
(0.5)
530.2
(76.9) 0.0
270.4
(60.8)
NWC S X X X
AM-3 359.3
(55.7)
68.9
(10.0) *
4.6
(0.7)
530.2
(76.9) 0.0
411.6
(92.5)
NWC S X X X
AM-4 359.3
(55.7)
68.9
(10.0) *
6.1
(1.0)
530.2
(76.9) 0.0
503.5
(113.2)
NWC S X X X
AH-2 359.3
(55.7)
86.9
(12.6) *
3.1
(0.5)
530.2
(76.9) 0.0
280.2
(63.0)
NWC S X X X
AH-3 359.3
(55.7)
86.9
(12.6) *
4.6
(0.7)
530.2
(76.9) 0.0
443.8
(99.8)
NWC S X X X
AH-4 359.3
(55.7)
86.9
(12.6) *
6.1
(1.0)
530.2
(76.9) 0.0
508.4
(114.3)
NWC S X X X
B1-4 359.3
(55.7)
73.1
(10.6) *
4.1
(0.6)
299.9
(43.5) 0.0
240.5
(54.1)
NWC S X X X
B2-2 359.3
(55.7)
84.8
(12.3) *
2.1
(0.3)
299.9
(43.5) 0.0
186.0
(41.8)
NWC S X X X
B2-4 359.3
(55.7)
84.8
(12.3) *
4.1
(0.6)
299.9
(43.5) 0.0
262.8
(60.0)
NWC S X X X
B2-5 359.3
(55.7)
84.8
(12.3) *
5.2
(0.8)
299.9
(43.5) 0.0
295.0
(66.3)
NWC S X X X
B2-6 359.3
(55.7)
84.8
(12.3) *
6.1
(1.0)
299.9
(43.5) 0.0
329.6
(74.1)
NWC S X X X
B3-4 359.3
(55.7)
95.1
(13.8) *
4.1
(0.6)
299.9
(43.5) 0.0
285.1
(64.1)
NWC S X X X
B4-2 359.3
(55.7)
106.2
(15.4) *
2.1
(0.3)
299.9
(43.5) 0.0
215.7
(48.5)
NWC S X X X
B4-4 359.3
(55.7)
106.2
(15.4) *
4.1
(0.6)
299.9
(43.5) 0.0
302.5
(68.0)
NWC S X X X
B4-5 359.3
(55.7)
106.2
(15.4) *
5.2
(0.8)
299.9
(43.5) 0.0
332.3
(74.7)
NWC S X X X
B4-6 359.3
(55.7)
106.2
(15.4) *
6.1
(1.0)
299.9
(43.5) 0.0
357.0
(80.27)
NWC S X X X
Banta 2005 [39]
12S-0L-0-
A 645.2
(100.0) 40.7
(5.9) 0.0 - 0.9
(0.2)
47.6
(10.7) LWC S X X
12S-0L-0-
B
645.2
(100.0)
40.7
(5.9)
0.0 - 0.9
(0.2)
84.5
(19.0)
LWC S X X
12S-2L-2-
A
645.2
(100.0)
40.7
(5.9)
2.8
(0.4)
496.4
(72.0)
0.9
(0.2)
185.0
(41.6)
LWC S X X X
12S-2L-2-
B
645.2
(100.0)
40.7
(5.9)
2.8
(0.4)
496.4
(72.0)
0.9
(0.2)
182.1
(40.9)
LWC S X X X
18S-1L-1-
A
1032.2
(160.0)
40.7
(5.9)
0.7
(0.1)
496.4
(72.0)
1.3
(0.3)
131.7
(29.6)
LWC S X X
18S-1L-1-
B
1032.2
(160.0)
40.7
(5.9)
0.7
(0.1)
496.4
(72.0)
1.3
(0.3)
114.8
(25.8)
LWC S X X
18S-2L-1-
A
1032.2
(160.0)
40.7
(5.9)
1.4
(0.2)
496.4
(72.0)
1.3
(0.3)
104.1
(23.4)
LWC S X X X
104
18S-2L-1-
B
1032.2
(160.0)
40.7
(5.9)
1.4
(0.2)
496.4
(72.0)
1.3
(0.3)
102.3
(23.0)
LWC S X X X
18S-2L-2-
A
1032.2
(160.0)
40.7
(5.9)
2.8
(0.4)
496.4
(72.0)
1.3
(0.3)
209.1
(47.0)
LWC S X X X
18S-2L-2-
B
1032.2
(160.0)
40.7
(5.9)
2.8
(0.4)
496.4
(72.0)
1.3
(0.3)
185.9
(41.8)
LWC S X X X
18S-2L-3-
A
1032.2
(160.0)
40.7
(5.9)
5.4
(0.7)
496.4
(72.0)
1.3
(0.3)
286.5
(64.4)
LWC S X X X
18S-2L-3-
B
1032.2
(160.0)
40.7
(5.9)
5.4
(0.7)
496.4
(72.0)
1.3
(0.3)
250.4
(56.3)
LWC S X X X
18S-0L-0-
A
1032.2
(160.0)
40.7
(5.9)
0.0 - 1.3
(0.3)
94.7
(21.3)
LWC S X X
18S-0L-0-
B
1032.2
(160.0)
40.7
(5.9)
0.0 - 1.3
(0.3)
72.9
(16.4)
LWC S X X
18C-0L-0-
A
1032.2
(160.0)
40.7
(5.9)
0.0 - 1.3
(0.3)
285.1
(64.1)
LWC R2 X X
18C-0L-0-
B
1032.2
(160.0)
40.7
(5.9)
0.0 - 1.3
(0.3)
222
(49.9)
LWC R2 X X
24S-0L-0-
A
1419.3
(220.0)
40.7
(5.9)
0.0 - 1.8
(0.4)
206.3
(46.4)
LWC S X X
24S-0L-0-
B
1419.3
(220.0)
40.7
(5.9)
0.0 - 1.8
(0.4)
222.4
(50.0)
LWC S X X
24S-2L-2-
A
1419.3
(220.0)
40.7
(5.9)
2.8
(0.4)
496.4
(72.0)
1.8
(0.4)
193.7
(43.5)
LWC S X X X
24S-2L-2-
B
1419.3
(220.0)
40.7
(5.9)
2.8
(0.4)
496.4
(72.0)
1.8
(0.4)
184.4
(41.4)
LWC S X X X
Kahn and Slapkus 2004 [24]
7_5 1529.0
(237.0)
50.1
(7.3)
4.8
(0.7)
556.4
(80.7)
0.0 625.1
(140.5)
NWC R2 X X X
7_7 1529.0
(237.0)
50.1
(7.3)
6.8
(1.0)
556.4
(80.7)
0.0 1035.1
(232.7)
NWC R2 X X X
7_9 1529.0
(237.0)
50.1
(7.3)
8.7
(1.3)
556.4
(80.7)
0.0 1055.1
(237.2)
NWC R2 X X X
Gohnert 2003 [40]
A-1 1041.1
(161.4)
22.8
(3.3) *
0.6
(0.1)
413.7
(60.0) 0.0
119.0
(26.7)
NWC R1 X X
A-2 1131.1
(175.3)
22.8
(3.3) *
0.6
(0.1)
413.7
(60.0) 0.0
75.0
(17.0)
NWC R1 X X
A-3 1135.3
(176.0)
22.8
(3.3)*
0.6
(0.1)
413.7
(60.0) 0.0
117.0
(26.3)
NWC R1 X X
A-4 1126.4
(174.6)
22.8
(3.3)*
0.6
(0.1)
413.7
(60.0) 0.0
141.0
(31.7)
NWC R1 X X
A-5 1126.4
(174.6)
22.8
(3.3)*
0.6
(0.1)
413.7
(60.0) 0.0
89.0
(20.0)
NWC R1 X X
A-6 1154.8
(179.0)
22.8
(3.3)*
0.6
(0.1)
413.7
(60.0) 0.0
100.0
(22.5)
NWC R1 X X
B-1 1141.3
(176.9)
22.8
(3.3)*
0.0 -
0.0
72.1
(16.2)
NWC R1 X X
B-2 1141.3
(176.9)
22.8
(3.3)*
0.0 -
0.0
123.1
(27.7)
NWC R1 X X
B-3 1141.3 22.8 0.0 - 0.0 103.1 NWC R1 X X
105
(176.9) (3.3)* (23.2)
B-4 1165.8
(180.7)
22.8
(3.3)*
0.0 -
0.0
146.9
(33.3)
NWC R1 X X
B-5 1045.1
(162.9)
22.8
(3.3)*
0.0 -
0.0
124.7
(28.6)
NWC R1 X X
B-6 1147.3
(177.8)
22.8
(3.3) *
0.0 -
0.0
124.7
(28.6)
NWC R1 X X
C-1 1145.2
(174.8)
25.5
(3.7)*
0.6
(0.1)
413.7
(60.0) 0.0
106.8
(24.3)
NWC R1 X X
C-2 1151.1
(176.7)
25.5
(3.7) *
0.6
(0.1)
413.7
(60.0) 0.0
155.0
(34.9)
NWC R1 X X
C-3 1144.2
(174.4)
25.5
(3.7)*
0.6
(0.1)
413.7
(60.0) 0.0
157.9
(35.5)
NWC R1 X X
C-4 1161.6
(176.7)
25.5
(3.7)*
0.6
(0.1)
413.7
(60.0) 0.0
220.2
(49.5)
NWC R1 X X
C-5 1124.4
(173.0)
25.5
(3.7)*
0.6
(0.1)
413.7
(60.0) 0.0
145.9
(32.8)
NWC R1 X X
C-6 1132.2
(173.9)
25.5
(3.7) *
0.6
(0.1)
413.7
(60.0) 0.0
219.3
(49.3)
NWC R1 X X
D-1 1163.9
(180.4)
31.4
(4.5) *
0.6
(0.1)
413.7
(60.0) 0.0
144.1
(32.4)
NWC R1 X X
D-2 1170.2
(181.3)
31.4
(4.5) *
0.6
(0.1)
413.7
(60.0) 0.0
149.0
(33.5)
NWC R1 X X
D-3 1163.9
(180.4)
31.4
(4.5) *
0.6
(0.1)
413.7
(60.0) 0.0
109.0
(24.5)
NWC R1 X X
D-4 1169.2
(182.0)
31.4
(4.5) *
0.6
(0.1)
413.7
(60.0) 0.0
135.2
(30.4)
NWC R1 X X
D-5 1163.9
(180.4)
31.4
(4.5) *
0.6
(0.1)
413.7
(60.0) 0.0
129.0
(29.0)
NWC R1 X X
D-6 1169.2
(182.0)
31.4
(4.5) *
0.6
(0.1)
413.7
(60.0) 0.0
148.1
(33.3)
NWC R1 X X
E-1 1155.2
(175.9)
29.2
(4.2) *
0.6
(0.1)
413.7
(60.0) 0.0
171.2
(38.5)
NWC R1 X X
E-2 1155.2
(175.9)
29.2
(4.2) *
0.6
(0.1)
413.7
(60.0) 0.0
176.1
(39.6)
NWC R1 X X
E-3 1155.2
(175.9)
29.2
(4.2) *
0.6
(0.1)
413.7
(60.0) 0.0
189.9
(42.7)
NWC R1 X X
E-4 1155.2
(175.9)
29.2
(4.2) *
0.6
(0.1)
413.7
(60.0) 0.0
135.2
(30.4)
NWC R1 X X
E-5 1155.2
(175.9)
29.2
(4.2) *
0.6
(0.1)
413.7
(60.0) 0.0
193.9
(43.6)
NWC R1 X X
E-6 1155.2
(175.9)
29.2
(4.2) *
0.6
(0.1)
413.7
(60.0) 0.0
193.9
(43.6)
NWC R1 X X
F-1 1155.2
(175.9)
23.9
(3.5) *
0.6
(0.1)
413.7
(60.0) 0.0
175.2
(38.7)
NWC R1 X X
F-2 1155.2
(175.9)
23.9
(3.5) *
0.6
(0.1)
413.7
(60.0) 0.0
173.2
(37.6)
NWC R1 X X
F-3 1165.2
(179.5)
23.9
(3.5) *
0.6
(0.1)
413.7
(60.0) 0.0
125.0
(28.1)
NWC R1 X X
F-4 1165.2
(179.5)
23.9
(3.5) *
0.6
(0.1)
413.7
(60.0) 0.0
175.2
(38.9)
NWC R1 X X
106
F-5 174.37 23.9
(3.5) *
0.6
(0.1)
413.7
(60.0) 0.0
148.1
(33.3)
NWC R1 X X
F-6 1155.2
(175.9)
23.9
(3.5) *
0.6
(0.1)
413.7
(60.0) 0.0
177.0
(39.8)
NWC R1 X X
G-1 1155.2
(175.9)
30.5
(4.4) *
0.6
(0.1)
413.7
(60.0) 0.0
173.0
(38.9)
NWC R1 X X
G-2 1155.2
(175.9)
30.5
(4.4) *
0.6
(0.1)
413.7
(60.0) 0.0
176.5
(39.1)
NWC R1 X X
G-3 1155.2
(175.9)
30.5
(4.4) *
0.6
(0.1)
413.7
(60.0) 0.0
175.2
(38.5)
NWC R1 X X
G-4 1165.2
(179.5)
30.5
(4.4) *
0.6
(0.1)
413.7
(60.0) 0.0
176.9
(39.4)
NWC R1 X X
G-5 1165.2
(179.5)
30.5
(4.4) *
0.6
(0.1)
413.7
(60.0) 0.0
176.9
(39.4)
NWC R1 X X
G-6 1155.2
(175.9)
30.5
(4.4) *
0.3
(0.04)
413.7
(60.0) 0.0
177.0
(39.8)
NWC R1 X X
H-1 1155.2
(175.9)
26.4
(3.8) *
0.3
(0.04)
413.7
(60.0) 0.0
172.1
(38.7)
NWC R1 X X
H-2 1155.2
(175.9)
26.4
(3.8) *
0.3
(0.04)
413.7
(60.0) 0.0
153.0
(34.4)
NWC R1 X X
H-3 1155.2
(175.9)
26.4
(3.8) *
0.3
(0.04)
413.7
(60.0) 0.0
144.1
(32.4)
NWC R1 X X
H-4 1240.8
(192.3)
26.4
(3.8) *
0.3
(0.04)
413.7
(60.0) 0.0
145.0
(32.6)
NWC R1 X X
H-5 1215.0
(188.3)
26.4
(3.8) *
0.3
(0.04)
413.7
(60.0) 0.0
147.2
(33.1)
NWC R1 X X
H-6 1215.0
(188.3)
26.4
(3.8) *
0.3
(0.04)
413.7
(60.0) 0.0
173.9
(39.1)
NWC R1 X X
I-1 864.5
(134.0)
25.3
(3.7) *
0.2
(0.03)
413.7
(60.0) 0.0
160.1
(36.0)
NWC R1 X X
I-2 864.5
(134.0)
25.3
(3.7) *
0.2
(0.03)
413.7
(60.0) 0.0
139.2
(31.3)
NWC R1 X X
I-3 864.5
(134.0)
25.3
(3.7) *
0.2
(0.03)
413.7
(60.0) 0.0
130.0
(29.2)
NWC R1 X X
I-4 864.5
(134.0)
25.3
(3.7) *
0.2
(0.03)
413.7
(60.0) 0.0
173.9
(39.1)
NWC R1 X X
I-5 864.5
(134.0)
25.3
(3.7) *
0.2
(0.03)
413.7
(60.0) 0.0
176.1
(39.6)
NWC R1 X X
I-6 864.5
(134.0)
25.3
(3.7) *
0.2
(0.03)
413.7
(60.0) 0.0
136.1
(30.6)
NWC R1 X X
J-1 189.07 29.6
(4.3) *
0.3
(0.04)
413.7
(60.0) 0.0
172.1
(38.7)
NWC R1 X X
J-2 1215.0
(188.3)
29.6
(4.3) *
0.3
(0.04)
413.7
(60.0) 0.0
155.2
(34.9)
NWC R1 X X
J-3 1215.0
(188.3)
29.6
(4.3) *
0.3
(0.04)
413.7
(60.0) 0.0
169.0
(38.0)
NWC R1 X X
J-4 1215.0
(188.3)
29.6
(4.3) *
0.3
(0.04)
413.7
(60.0) 0.0
153.9
(34.6)
NWC R1 X X
J-5 1215.0
(188.3)
29.6
(4.3) *
0.3
(0.04)
413.7
(60.0) 0.0
138.3
(31.3)
NWC R1 X X
J-6 1215.0
(188.3)
29.6
(4.3) *
0.3
(0.04)
413.7
(60.0) 0.0
153.0
(34.4)
NWC R1 X X
107
K-1 890.3
(138.3)
29.6
(4.3) *
0.2
(0.03)
413.7
(60.0) 0.0
173.9
(39.1)
NWC R1 X X
K-2 890.3
(138.3)
29.6
(4.3) *
0.2
(0.03)
413.7
(60.0) 0.0
168.1
(37.8)
NWC R1 X X
K-3 890.3
(138.3)
29.6
(4.3) *
0.2
(0.03)
413.7
(60.0) 0.0
173.0
(38.9)
NWC R1 X X
K-4 890.3
(138.3)
29.6
(4.3) *
0.2
(0.03)
413.7
(60.0) 0.0
177.0
(39.8)
NWC R1 X X
K-5 890.3
(138.3)
29.6
(4.3) *
0.2
(0.03)
413.7
(60.0) 0.0
135.2
(30.4)
NWC R1 X X
K-6 890.3
(138.3)
29.6
(4.3) *
0.2
(0.03)
413.7
(60.0) 0.0
165.0
(37.1)
NWC R1 X X
L-1 1148.4
(178.8)
33.9
(4.9) *
0.3
(0.04)
413.7
(60.0) 0.0
181.0
(40.7)
NWC R1 X X
L-2 1148.4
(178.8)
33.9
(4.9) *
0.3
(0.04)
413.7
(60.0) 0.0
181.0
(40.7)
NWC R1 X X
L-3 1148.4
(178.8)
33.9
(4.9) *
0.3
(0.04)
413.7
(60.0) 0.0
189.0
(42.5)
NWC R1 X X
L-4 1148.4
(178.8)
33.9
(4.9) *
0.3
(0.04)
413.7
(60.0) 0.0
189.0
(41.6)
NWC R1 X X
L-5 1148.4
(178.8)
33.9
(4.9) *
0.2
(0.03)
413.7
(60.0) 0.0
189.0
(42.5)
NWC R1 X X
L-6 1148.4
(178.8)
33.9
(4.9) *
0.3
(0.04)
413.7
(60.0) 0.0
188.2
(42.3)
NWC R1 X X
M-1 1148.4
(178.8)
29.6
(4.3) *
0.3
(0.04)
413.7
(60.0) 0.0
179.3
(40.3)
NWC R1 X X
M-2 1148.4
(178.8)
29.6
(4.3) *
0.3
(0.04)
413.7
(60.0) 0.0
164.1
(36.9)
NWC R1 X X
M-3 1167.8
(181.1)
29.6
(4.3) *
0.3
(0.04)
413.7
(60.0) 0.0
201.1
(45.2)
NWC R1 X X
M-4 1167.8
(181.1)
29.6
(4.3) *
0.3
(0.04)
413.7
(60.0) 0.0
179.3
(40.3)
NWC R1 X X
M-5 1167.8
(181.1)
29.6
(4.3) *
0.3
(0.04)
413.7
(60.0) 0.0
178.3
(40.0)
NWC R1 X X
M-6 1167.8
(181.1)
29.6
(4.3) *
0.3
(0.04)
413.7
(60.0) 0.0
153.9
(34.6)
NWC R1 X X
N-1 1851.6
(287.9)
38.3
(5.6) *
0.2
(0.03)
413.7
(60.0) 0.0
175.2
(39.4)
NWC R1 X X
N-2 1851.6
(287.9)
38.3
(5.6) *
0.2
(0.03)
413.7
(60.0) 0.0
140.1
(31.5)
NWC R1 X X
N-3 1851.6
(287.9)
38.3
(5.6) *
0.2
(0.03)
413.7
(60.0) 0.0
179.3
(40.3)
NWC R1 X X
N-4 1851.6
(287.9)
38.3
(5.6) *
0.2
(0.03)
413.7
(60.0) 0.0
175.2
(39.4)
NWC R1 X X
N-5 1851.6
(287.9)
38.3
(5.6) *
0.2
(0.03)
413.7
(60.0) 0.0
179.3
(40.3)
NWC R1 X X
N-6 1851.6
(287.9)
38.3
(5.6) *
0.2
(0.03)
413.7
(60.0) 0.0
167.2
(37.6)
NWC R1 X X
O-1 1851.6
(287.9)
28.2
(4.1) *
0.2
(0.03)
413.7
(60.0) 0.0
149.0
(33.5)
NWC R1 X X
O-2 1367.7
(212.4)
28.2
(4.1) *
0.2
(0.03)
413.7
(60.0) 0.0
69.8
(15.7)
NWC R1 X X
108
O-3 1309.7
(204.0)
28.2
(4.1) *
0.2
(0.03)
413.7
(60.0) 0.0
120.1
(27.0)
NWC R1 X X
O-4 1309.7
(204.0)
28.2
(4.1) *
0.2
(0.03)
413.7
(60.0) 0.0
120.1
(27.0)
NWC R1 X X
O-5 1309.7
(204.0)
28.2
(4.1) *
0.2
(0.03)
413.7
(60.0) 0.0
125.0
(28.1)
NWC R1 X X
O-6 1896.8
(294.5)
28.2
(4.1) *
0.2
(0.03)
413.7
(60.0) 0.0
177.0
(39.8)
NWC R1 X X
Kahn and Mitchell 2002 [10] SF-7-1-CJ 929.0
(144.0)
64.5
(9.3)
0.7
(0.1)
572.3
(83.0) 0.0
240.2
(54.0)
NWC R2 X X
SF-7-2-CJ 929.0
(144.0)
64.5
(9.3)
1.1
(0.2)
572.3
(83.0) 0.0
365.2
(82.1)
NWC R2 X X X
SF-7-3-CJ 929.0
(144.0)
70.7
(10.3)
2.1
(0.3)
572.3
(83.0) 0.0
490.6
(110.3)
NWC R2 X X X
SF-7-4-CJ 929.0
(144.0)
70.7
(10.3)
2.8
(0.4)
572.3
(83.0) 0.0
590.3
(132.7)
NWC R2 X X X
SF-10-1-
CJ
929.0
(144.0)
76.7
(11.1)
0.7
(0.1)
572.3
(83.0) 0.0
141.0
(31.7)
NWC R2 X X
SF-10-2-
CJ
929.0
(144.0)
65.6
(9.5)
1.1
(0.2)
572.3
(83.0) 0.0
219.3
(49.3)
NWC R2 X X X
SF-10-3-
CJ
929.0
(144.0)
65.6
(9.5)
2.1
(0.3)
572.3
(83.0) 0.0
506.6
(113.9)
NWC R2 X X X
SF-10-4-
CJ
929.0
(144.0)
65.6
(9.5)
2.8
(0.4)
572.3
(83.0) 0.0
560.5
(126.0)
NWC R2 X X X
SF-14-1-
CJ
929.0
(144.0)
88.2
(12.8)
0.7
(0.1)
572.3
(83.0) 0.0
404.3
(90.9)
NWC R2 X X
SF-14-2-
CJ
929.0
(144.0)
88.2
(12.8)
1.1
(0.2)
572.3
(83.0) 0.0
441.3
(99.2)
NWC R2 X X X
SF-14-3-
CJ
929.0
(144.0)
86.2
(12.5)
2.1
(0.3)
572.3
(83.0) 0.0
599.2
(134.7)
NWC R2 X X X
SF-14-4-
CJ
929.0
(144.0)
86.2
(12.5)
2.8
(0.4)
572.3
(83.0) 0.0
681.0
(153.1)
NWC R2 X X X
SF-4-1-U 929.0
(144.0)
46.9
(6.8)
0.7
(0.1)
479.2
(69.5) 0.0
257.5
(57.9)
NWC M X
SF-4-2-U 929.0
(144.0)
46.9
(6.8)
1.1
(0.2)
479.2
(69.5) 0.0
356.3
(80.1)
NWC M X X
SF-4-3-U 929.0
(144.0)
46.9
(6.8)
2.1
(0.3)
479.2
(69.5) 0.0
381.6
(85.8)
NWC M X X
SF-7-1-U 929.0
(144.0)
80.9
(11.7)
0.7
(0.1)
572.3
(83.0) 0.0
389.2
(87.5)
NWC M X
SF-7-2-U 929.0
(144.0)
85.6
(12.4)
1.1
(0.2)
572.3
(83.0) 0.0
525.3
(118.1)
NWC M X X
SF-7-3-U 929.0
(144.0)
90.3
(13.1)
2.1
(0.3)
572.3
(83.0) 0.0
615.6
(138.4)
NWC M X X
SF-7-4-U 929.0
(144.0)
86.0
(12.5)
2.8
(0.4)
572.3
(83.0) 0.0
663.2
(149.1)
NWC M X X
SF-10-1-
U-a
929.0
(144.0)
83.1
(12.0)
0.7
(0.1)
572.3
(83.0) 0.0
445.3
(100.1)
NWC M X
SF-10-1-
U-b
929.0
(144.0)
98.8
(14.3)
0.7
(0.1)
572.3
(83.0) 0.0
408.8
(91.9)
NWC M X
109
SF-10-2-
U-a
929.0
(144.0)
101.2
(14.7)
1.1
(0.2)
572.3
(83.0) 0.0
580.9
(130.6)
NWC M X X
SF-10-2-
U-b
929.0
(144.0)
101.2
(14.7)
1.1
(0.2)
572.3
(83.0) 0.0
551.6
(124.0)
NWC M X X
SF-10-3-
U-a
929.0
(144.0)
111.7
(16.2)
2.1
(0.3)
572.3
(83.0) 0.0
644.1
(144.8)
NWC M X X
SF-10-3-
U-b
929.0
(144.0)
96.0
(13.9)
2.1
(0.3)
572.3
(83.0) 0.0
657.9
(147.9)
NWC M X X
SF-10-4-
U-a
929.0
(144.0)
106.9
(15.5)
2.8
(0.4)
572.3
(83.0) 0.0
693.9
(156.0)
NWC M X X
SF-10-4-
U-b
929.0
(144.0)
113.6
(16.5)
2.8
(0.4)
572.3
(83.0) 0.0
711.7
(160.0)
NWC M X X
SF-14-1-
U
929.0
(144.0)
120.6
(17.5)
0.7
(0.1)
572.3
(83.0) 0.0
422.1
(94.9)
NWC M X
SF-14-2-
U
929.0
(144.0)
120.6
(17.5)
1.1
(0.2)
572.3
(83.0) 0.0
482.6
(108.5)
NWC M X X
SF-14-3-
U
929.0
(144.0)
111.4
(16.3)
2.1
(0.3)
572.3
(83.0) 0.0
650.3
(146.2)
NWC M X X
SF-14-4-
U
929.0
(144.0)
111.4
(16.3)
2.8
(0.4)
572.3
(83.0) 0.0
693.9
(156.0)
NWC M X X
Gohnert 2000 [13] 1 1122.9
(174.0)
21.4
(3.3)
0.0 -
0.0
117.9
(26.5)
NWC R1 X X
2 1122.9
(174.0)
21.4
(3.3)
0.0 -
0.0
77.4
(17.4)
NWC R1 X X
3 1122.9
(174.0)
21.4
(3.3)
0.0 -
0.0
115.6
(26.0)
NWC R1 X X
4 1122.9
(174.0)
21.4
(3.3)
0.0 -
0.0
140.3
(31.5)
NWC R1 X X
5 1122.9
(174.0)
21.4
(3.3)
0.0 -
0.0
86.5
(19.9)
NWC R1 X X
6 1122.9
(174.0)
21.4
(3.3)
0.0 -
0.0
97.7
(22.0)
NWC R1 X X
7 1122.9
(174.0)
31.4
(4.5)
0.0 -
0.0
139.3
(31.3)
NWC R1 X X
8 1122.9
(174.0)
31.4
(4.5)
0.0 -
0.0
139.3
(31.3)
NWC R1 X X
9 1122.9
(174.0)
31.4
(4.5)
0.0 -
0.0
108.4
(24.4)
NWC R1 X X
10 1122.9
(174.0)
31.4
(4.5)
0.0 -
0.0
131.7
(29.6)
NWC R1 X X
11 1122.9
(174.0)
31.4
(4.5)
0.0 -
0.0
123.9
(27.8)
NWC R1 X X
12 1122.9
(174.0)
31.4
(4.5)
0.0 -
0.0
139.3
(31.3)
NWC R1 X X
Valluvan et al. 1999 [42]
B1 825.8
(128.0)
24.1
(3.5)
8.5
(1.3)
475.7
(69.0) 0.0
502
(113.0)
NWC R2 X X X
B2 825.8
(128.0)
24.1
(3.5)
17.0
(2.6)
475.7
(69.0) 0.0
578.3
(130.0)
NWC R2 X X X
B3 825.8 24.1 0.0 - 569.4 1129.8 NWC R2 X X
110
(128.0) (3.5) (128.0) (254.0)
B4 825.8
(128.0)
24.1
(3.5)
0.0 - 854.0
(192.0)
1294.4
(291.0)
NWC R2 X X
B5 825.8
(128.0)
24.1
(3.5)
8.5
(1.3)
475.7
(69.0)
569.4
(128.0)
1175.3
(264.0)
NWC R2 X X X
B6 825.8
(128.0)
24.1
(3.5)
17.0
(2.6)
475.7
(69.0)
569.4
(128.0)
1218.8
(274.0)
NWC R2 X X X
B9 825.8
(128.0)
24.1
(3.5)
8.5
(1.3)
475.7
(69.0)
199.3
(44.8)
742.8
(167.0)
NWC R2 X X X
Loov and Patnaik 1994 [22]
1 894.5
(138.6)
37.4
(5.4)
24.1
(3.7)
437.9
(63.5) 0.0
690.8
(155.3)
NWC R2 X X X
2 894.5
(138.6)
34.9
(5.1)
9.9
(1.5)
437.9
(63.5) 0.0
382.3
(86.0)
NWC R2 X X X
3 894.5
(138.6)
30.5
(4.4)
15.6
(2.4)
431.9
(62.6) 0.0
610.7
(137.3)
NWC R2 X X X
5 894.5
(138.6)
34.7
(5.0)
9.9
(1.5)
431.9
(62.6) 0.0
493.3
(110.9)
NWC R2 X X X
6 894.5
(138.6)
37.1
(5.4)
9.9
(1.5)
428.0
(62.1) 0.0
468.7
(105.4)
NWC R2 X X X
7 894.5
(138.6)
35.8
(5.2)
34.1
(5.3)
431.9
(62.6) 0.0
826.4
(185.8)
NWC R2 X X X
8 1789.0
(277.3)
35.6
(5.2)
9.9
(1.5)
407.0
(59.0) 0.0
555.1
(124.8)
NWC R2 X X X
9 894.5
(138.6)
37.1
(5.4)
7.1
(1.1)
431.9
(62.6) 0.0
413.2
(92.9)
NWC R2 X X X
10 1789.0
(277.3)
37.6
(5.4)
7.1
(1.1)
407.9
(59.2) 0.0
616.7
(138.6)
NWC R2 X X X
11 3581.1
(555.1)
32.7
(4.7)
7.1
(1.1)
420.0
(60.9) 0.0
913.7
(205.4)
NWC R2 X X X
12 894.5
(138.6)
34.6
(5.0)
34.1
(5.3)
407.9
(59.2) 0.0
820.2
(184.4)
NWC R2 X X X
13 1789.0
(277.3)
19.2
(2.8)
7.1
(1.1)
431.9
(62.6) 0.0
518.2
(116.5)
NWC R2 X X
14 1789.0
(277.3)
19.6
(2.8)
7.1
(1.1)
431.9
(62.6) 0.0
345.3
(77.6)
NWC S X X
Hsu et al. 1987 [11] 1.1 A 541.9
(84.0)
27.0
(3.9)
2.4
(0.4)
349.6
(50.7) 0.0
280.2
(63.0)
NWC R2 X X X
1.1 B 541.9
(84.0)
29.9
(4.3)
2.4
(0.4)
331.0
(48.0) 0.0
315.4
(70.9)
NWC R2 X X X
1.2 A 541.9
(84.0)
27.0
(3.9)
4.5
(0.7)
349.6
(50.7) 0.0
373.6
(84.0)
NWC R2 X X X
1.2 B 541.9
(84.0)
29.0
(4.2)
4.5
(0.7)
331.0
(48.0) 0.0
366.2
(82.3)
NWC R2 X X X
1.3 A 541.9
(84.0)
27.0
(3.9)
7.2
(1.1)
349.6
(50.7) 0.0
411.0
(92.4)
NWC R2 X X X
1.3 B 541.9
(84.0)
27.0
(3.9)
7.2
(1.1)
331.0
(48.0) 0.0
399.8
(89.9)
NWC R2 X X X
1.4 A 541.9
(84.0)
31.1
(4.5)
9.5
(1.5)
349.6
(50.7) 0.0
508.2
(114.2)
NWC R2 X X X
111
1.4 B 541.9
(84.0)
27.0
(3.9)
9.5
(1.5)
331.0
(48.0) 0.0
478.3
(107.5)
NWC R2 X X X
1.5 A 541.9
(84.0)
31.1
(4.5)
11.9
(1.8)
349.6
(50.7) 0.0
520.4
(117.6)
NWC R2 X X X
1.5 B 541.9
(84.0)
28.3
(4.1)
11.9
(1.8)
331.0
(48.0) 0.0
515.5
(115.9)
NWC R2 X X X
1.6 A 541.9
(84.0)
29.9
(4.3)
14.3
(2.2)
349.6
(50.7) 0.0
533.7
(120.1)
NWC R2 X X X
1.6 B 541.9
(84.0)
28.3
(4.1)
14.3
(2.2)
331.0
(48.0) 0.0
530.6
(119.3)
NWC R2 X X X
6.1 541.9
(84.0)
27.0
(3.9)
2.4
(0.4)
331.0
(48.0) 0.0
298.9
(67.2)
NWC R2 X X X
6.2 541.9
(84.0)
27.0
(3.9)
11.9
(1.8)
331.0
(48.0) 0.0
463.5
(104.2)
NWC R2 X X X
M1 541.9
(84.0)
29.0
(4.2)
2.4
(0.4)
349.6
(50.7) 0.0
284.0
(63.8)
NWC R2 X X X
M2 541.9
(84.0)
27.0
(3.9)
5.0
(0.7)
363.3
(52.7) 0.0
366.2
(82.3)
NWC R2 X X X
M3 541.9
(84.0)
27.6
(4.0)
7.2
(1.1)
363.3
(52.7) 0.0
414.7
(93.2)
NWC R2 X X X
M4 541.9
(84.0)
28.3
(4.1)
9.5
(1.5)
349.6
(50.7) 0.0
426.0
(95.8)
NWC R2 X X X
M5 541.9
(84.0)
27.0
(3.9)
11.9
(1.8)
363.3
(52.7) 0.0
478.3
(107.5)
NWC R2 X X X
M6 541.9
(84.0)
28.3
(4.1)
14.3
(2.2)
363.3
(52.7) 0.0
493.3
(110.9)
NWC R2 X X X
E1U 541.9
(84.0)
28.3
(4.1)
5.7
(0.9)
363.3
(52.7) 0.0
407.3
(91.6)
NWC R2 X X X
E4U 541.9
(84.0)
27.0
(3.9)
5.7
(0.9)
338.5
(49.1)
74.7
(16.8)
351.2
(79.0)
NWC R2 X X X
E6U 541.9
(84.0)
28.3
(4.1)
5.7
(0.9)
349.6
(50.7)
149.5
(33.6)
227.7
(51.2)
NWC R2 X X X
F1U 541.9
(84.0)
27.6
(4.0)
8.5
(1.3)
360.0
(52.2) 0.0
512.0
(115.1)
NWC R2 X X X
F4U 541.9
(84.0)
29.0
(4.2)
8.5
(1.3)
366.8
(53.2)
74.7
(16.8)
426.0
(95.8)
NWC R2 X X X
F6U 541.9
(84.0)
29.0
(4.2)
8.5
(1.3)
351.6
(51.0)
149.5
(33.6)
396.1
(89.0)
NWC R2 X X X
Mattock et al. 1976 [25] A0 322.6
(50.0)
29.2
(4.2)
0.0 - 0.0 111.2
(25.0)
LWC M X
A1 322.6
(50.0)
25.8
(3.7)
1.4
(0.2)
328.9
(47.7)
0.0 168.8
(37.9)
LWC M X X
A2 322.6
(50.0)
28.3
(4.1)
2.8
(0.4)
369.6
(53.6)
0.0 203.3
(45.7)
LWC M X X
A3 322.6
(50.0)
27.0
(3.9)
5.3
(0.7)
366.8
(53.2)
0.0 226.8
(51.0)
LWC M X X
A4 322.6
(50.0)
28.3
(4.1)
6.5
(0.9)
350.9
(50.9)
0.0 244.6
(55.0)
LWC M X X
A5 322.6
(50.0)
27.3
(4.0)
7.1
(1.1)
350.9
(50.9)
0.0 264.7
(59.5)
LWC M X X
112
A6 322.6
(50.0)
29.2
(4.2)
8.5
(1.3)
357.1
(51.8)
0.0 298.9
(67.2)
LWC M X X
E1 322.6
(50.0)
28.3
(4.1)
1.4
(0.2)
360.6
(52.3)
0.0 173.5
(39.0)
LWC M X X
E2 322.6
(50.0)
27.3
(4.0)
2.8
(0.4)
360.6
(52.3)
0.0 193.9
(43.6)
LWC M X X
E3 322.6
(50.0)
28.3
(4.1)
5.3
(0.7)
360.6
(52.3)
0.0 213.5
(48.0)
LWC M X X
E4 322.6
(50.0)
27.3
(4.0)
6.5
(0.9)
366.8
(53.2)
0.0 255.8
(57.5)
LWC M X X
E5 322.6
(50.0)
28.3
(4.1)
7.1
(1.1)
348.2
(50.5)
0.0 267.9
(60.0)
LWC M X X
E6 322.6
(50.0)
27.3
(4.0)
8.5
(1.3)
360.6
(52.3)
0.0 298.1
(62.5)
LWC M X X
G0 322.6
(50.0)
27.3
(4.0)
0.0 - 0.0 117.9
(26.5)
LWC M X
G1 322.6
(50.0)
28.3
(4.1)
1.4
(0.2)
360.6
(52.3)
0.0 182.4
(41.0)
LWC M X X
G2 322.6
(50.0)
25.8
(3.7)
2.8
(0.4)
348.2
(50.5)
0.0 188.1
(42.3)
LWC M X X
G3 322.6
(50.0)
28.3
(4.1)
5.3
(0.7)
357.1
(51.8)
0.0 235.7
(53.0)
LWC M X X
G4 322.6
(50.0)
30.5
(4.4)
6.5
(0.9)
346.8
(53.2)
0.0 255.8
(57.5)
LWC M X X
G5 322.6
(50.0)
27.3
(4.0)
7.1
(1.1)
357.1
(51.8)
0.0 253.5
(57.0)
LWC M X X
G6 322.6
(50.0)
27.3
(4.0)
8.5
(1.3)
357.1
(51.8)
0.0 264.7
(59.5)
LWC M X X
M0 322.6
(50.0)
27.1
(3.9)
0.0 - 0.0 131.2
(29.5)
LWC M X
M1 322.6
(50.0)
29.2
(4.2)
1.4
(0.2)
350.9
(50.9)
0.0 169.0
(38.0)
LWC M X X
M2 322.6
(50.0)
27.1
(3.9)
2.8
(0.4)
363.3
(52.7)
0.0 218.0
(49.0)
LWC M X X
M3 322.6
(50.0)
27.3
(4.0)
5.3
(0.7)
360.6
(52.3)
0.0 246.9
(55.5)
LWC M X X
M4 322.6
(50.0)
28.3
(4.1)
6.5
(0.9)
350.9
(50.9)
0.0 253.5
(57.0)
LWC M X X
M5 322.6
(50.0)
27.1
(3.9)
7.1
(1.1)
363.3
(52.7)
0.0 284.7
(64.0)
LWC M X X
M6 322.6
(50.0)
28.3
(4.1)
8.5
(1.3)
363.3
(52.7)
0.0 293.6
(66.0)
LWC M X X
Mattock et al. 1975 [49]
E1U 541.9
(84.0)
28.0
(4.1)
5.7
(0.9)
363.3
(52.7) 0.0
406.9
(91.5)
NWC M X X
E4U 541.9
(84.0)
26.6
(3.9)
5.7
(0.9)
338.5
(49.1)
74.7
(16.8)
353.4
(79.5)
NWC M X X
E6U 541.9
(84.0)
28.4
(4.1)
5.7
(0.9)
351.6
(51.0)
149.5
(33.6)
226.8
(51.0)
NWC M X X
F4C 541.9
(84.0)
26.6
(3.9)
8.5
(1.3)
351.6
(51.0)
74.7
(16.8)
313.6
(70.5)
NWC M X X
113
F1U 541.9
(84.0)
27.6
(4.0)
8.5
(1.3)
359.9
(52.2) 0.0
511.5
(115.0)
NWC M X X
F4U 541.9
(84.0)
28.0
(4.1)
8.5
(1.3)
366.8
(53.2)
74.7
(16.8)
427.0
(96.0)
NWC M X X
F6U 541.9
(84.0)
29.2
(4.2)
8.5
(1.3)
351.6
(51.0)
149.5
(33.6)
398.1
(89.5)
NWC M X X
Mattock and Hawkins 1972 [7]
9.1 464.5
(72.0)
37.9
(5.5)
7.1
(1.1)
361.3
(52.4)
787.3
(177.0)
787.9
(177.1)
NWC M X X
9.2 464.5
(72.0)
37.9
(5.5)
8.5
(1.3)
359.9
(52.2)
473.3
(106.4)
819.9
(184.3)
NWC M X X
9.3 464.5
(72.0)
27.2
(3.9)
8.5
(1.3)
360.6
(52.3)
129.4
(29.1)
483.6
(108.7)
NWC M X X
9.4 464.5
(72.0)
27.2
(3.9)
8.5
(1.3)
370.2
(53.7) 0.0
442.1
(99.4)
NWC M X X
9.5 464.5
(72.0)
44.4
(6.4)
5.7
(0.9)
351.6
(51.0)
530.2
(119.2)
919. 6
(206.6)
NWC M X X
9.6 464.5
(72.0)
44.4
(6.4)
2.8
(0.4)
351.6
(51.0)
512.0
(115.1)
887.1
(199.4)
NWC M X X
Hofbeck et al. 1969 [6]
1,0 322.6
(50.0)
27.8
(4.0)
0.0 -
0.0
106.7
(24.0)
NWC M X
1.1A 322.6
(50.0)
27.0
(3.9)
1.4
(0.2)
349.6
(50.7) 0.0
162.4
(37.5)
NWC M X X
1.1B 322.6
(50.0)
29.9
(4.3)
1.4
(0.2)
330.9
(48.0) 0.0
186.8
(42.0)
NWC M X X
1.2A 322.6
(50.0)
26.5
(3.8)
2.8
(0.4)
349.6
(50.7) 0.0
222.4
(50.0)
NWC M X X
1.2B 322.6
(50.0)
27.0
(3.9)
2.8
(0.4)
330.9
(48.0) 0.0
218.0
(49.0)
NWC M X X
1.3A 322.6
(50.0)
31.1
(4.5)
4.2
(0.7)
349.6
(50.7) 0.0
244. 6
(55.0)
NWC M X X
1.3B 322.6
(50.0)
26.5
(3.8)
4.2
(0.7)
330.9
(48.0) 0.0
238.0
(53.5)
NWC M X X
1.4A 322.6
(50.0)
31.1
(4.5)
5.7
(0.9)
349.6
(50.7) 0.0
302.5
(68.0)
NWC M X X
1.4B 322.6
(50.0)
26.5
(3.8)
5.7
(0.9)
330.9
(48.0) 0.0
284.7
(64.0)
NWC M X X
1.5A 322.6
(50.0)
31.1
(4.5)
7.1
(1.1)
349.6
(50.7) 0.0
311.4
(70.0)
NWC M X X
1.5B 322.6
(50.0)
28.3
(4.1)
7.1
(1.1)
330.9
(48.0) 0.0
306.9
(69.0)
NWC M X X
1.6A 322.6
(50.0)
29.6
(4.3)
8.5
(1.3)
349.6
(50.7) 0.0
318.0
(71.5)
NWC M X X
1.6B 322.6
(50.0)
27.6
(4.0)
8.5
(1.3)
330.9
(48.0) 0.0
315.8
(71.0)
NWC M X X
6.1 322.6
(50.0)
27.6
(4.0)
1.4
(0.2)
330.9
(48.0) 0.0
177.9
(40.0)
NWC M X X
6.2 322.6
(50.0)
27.0
(3.9)
7.1
(1.1)
330.9
(48.0) 0.0
275.8
(62.0)
NWC M X X
114
* was tested using cube specimens. They were converted to cylinder results to
comparison in the database.
**NWC= Both sides are normal weight concrete; and LWC= At least one side is
lightweight concrete
***M=Monolithic; S= Smooth interface; R1= Intentionally roughened interface test with
amplitude less than 6mm; and R2= Intentionally roughened interface test with amplitude
more than or equal to 6mm
Recommended